WO1980002766A1 - Method of calculation of polynomials by accumulation and apparatus therefor,and method of synthesizing musical tone waveforms by means of the system - Google Patents

Abstract

Arithmetic operations of various functions by means of polynomials and specifically to synthesize of various waveforms of musical tone by accumulation method. The values f(kX) of the polynomial f(x) = a0 + a1x1 + a2x2 + .... + aNxN (where aN = O, and N is an integer larger than unity) for equi-spaced discrete values x = kX (where X is a real number, and k = 0, 1, 2, 3...) may be operated for a step parameter k through the following sequences: (N + 1) of registers RO to RN and at least one adder are provided. With making use of the coefficients of each term a0, a1, a2..... aN of the polynomial f(x), the first coefficient C which is given to be accumulated in the register R1 and initial values for each register R1 to RN are determined so that the content (RN)k of the register RN for k-th step may be equal to the value of f(kX). Then, the first coefficient C and each initial value (R1)0 to (RN)0 are set in each register RO to RN, and thus the accumulating operations (R1)k + 1 = (R1)k + C, (R2) k+ 1 = (R2)k + (R1)k, (R3)k + 1 = (R3)k + (R2)k, ..... (RN)k + 1 = (RN)k + (RN-1)k are carried out in the adder, whereby at the k-th step, the accumulated value f(kX) may be obtained as the content (RN)k of the register Rk. Such accumulation may facilitate easier operation of various functions or generation of various waveforms.

Description

 Specification

 Title of the invention Polynomial calculation method by cumulative addition and its device and musical tone waveform generation method using the method '' Technical Field

 The present invention relates to a calculation method using a polynomial of various functions using the cumulative addition method, a device therefor, and a method of creating a tone waveform to which the cumulative addition method is applied.

 Background technology

 It is widely used in the field of applied mathematics, for example, to calculate the approximate value of a function by expanding the function into a polynomial when performing an approximate calculation. .. Especially graphics

 In the fields that require numerical calculation such as (raphi cs), approximate calculation of the function by this polynomial is frequently performed.

 Multiplying polynomials requires multiplication, and since multiplying operations occupy most of the calculation time, it is desirable to reduce the number of multiplying operations in polynomial computing. It is. Consider, for example, the case of calculating the following polynomial / (X).

/ (x) = ax + bx ³ + cx ⁵ …-(1)

 It seems that the calculation of the polynomial on the right-hand side of Eq. (1) requires 6 multiplications at first glance, but it is also possible to factor Eq. (1) as follows. It is clear that a small number of calculations is required.

ax + bx ³ + cx ^J = x (a + x ² (b + cx ² )) (2)

 That is, in order to calculate the right side of Eq. (2), it is sufficient to perform factorization four times if it is factorized in advance.

OMPI. This method is well known, and is usually adopted in order to reduce the number of operations in a computer software.

 Under certain conditions, if we can find the value of the polynomial for a particular value of X, we have.

 The specific condition here is the case where the sequential t-calculation is performed on the equally spaced discrete values of X. That is, this is the case when the polynomial is successively calculated for the value of ¾ = nx (n = 0, 1, 2,… :).

For example, the successive calculation of sin () is

is there . This can also be used in the field of graphs (gr a p h i c s), which illustrates the relationship between x and y, where χ is the horizontal axis and y is the vertical axis for the polynomial y = f i x).

 Moreover, this can be considered to be used in the case of applying to the generation of musical tone waveforms. If the tone waveform is a repeating waveform of the same waveform, it is sufficient to create a waveform corresponding to one cycle of the waveform. That is, if an arbitrary function in a given interval can be calculated, then an arbitrary repeated waveform can be obtained by repeating the calculation of that function. Considering that an arbitrary function in a given interval can be expanded into a polynomial approximately, it is natural that the effect of using this principle to generate a tone waveform is great. Clarity

 In a conventional electronic musical instrument, when a waveform is calculated by a digital method to generate a musical tone waveform, the waveform function to be generated, for example, the si li e function or the The approximate function is ¾:

 O PI

^ It was calculated using the pull-up loop method or the multiplication t. Its calculation speed satisfies the sampling theorem, so that, for example, when synthesizing a waveform containing frequency components up to 20 kHz, the sampling frequency of 40 kHz is used. It has been adopted by using a dull one. The table-up method is a read-only memory, ROM, or ROM that stores the values of functions when the values of variables are changed sequentially. Say how to read. In order to obtain a waveform with sufficient accuracy using this method, a ROM with a large storage capacity is required, and the current LSI technology is expensive to manufacture. For this reason, the interpolation method is generally used to obtain the intermediate value that is not stored in the ROM.

 -For example, if we raise a function such as sin (χ. + Δχ) and expand it, we can expand it to the first and second terms, and we can expand it as Eq. (3).

 sin (X 0 + Δ X == sin X 0 + Δ x · cos x o (3)

 The right side of Eq. (3) can be operated by two tables, a single table and a costable table, and multiplication and addition. In other words, from the ROM that stores sin x and cos x for various values of X (these are called single and co-single), x = xo. ;]] Then read sin χο ヽ cos xo and calculate sin χ. + Δχ 'cos X. to obtain sin (xo + Δχ) which is the sign of the sign'-table. Thus, the internal method requires-multiplication and addition, and it requires both the tape '' and the operation to improve the precision.

 In addition, when calculating and generating a waveform using the digital method,

OMPI In the case of audio signals such as musical tones, it is usually necessary to have a high shunt of 40 kHz or more: ° ling rate in order to prevent fold over. This folding is a phenomenon that occurs when the number of samples contained in one cycle of the waveform does not become an integer when sampling an arbitrary repeated waveform.

 Therefore, if the number of samples is set to be a complete integer for one waveform of all frequencies required for a musical sound, the problem of this return]) will occur. By doing this, it is possible to reduce the sampling rate sufficiently. This sample rate depends on the highest frequency of the required fundamental tone. For example, if the highest frequency is 2 kHz, the sample rate is 4 kHz and the highest frequency is 4 kHz. If the sampling rate is kHz, the sampling rate will be 8 kHz.

 An object of the present invention is to provide a polynomial calculation method and an apparatus thereof, which have a small calculation scale and can perform calculations without using a very small number of multiplications or multiplications at all.

 Another object of the present invention is not based on the table-and-loop method, and therefore does not require a large-scale ROM and can be constructed with high accuracy and at low cost. A method and an apparatus therefor are provided. -Disclosure of invention

 According to the present invention, according to the multi-step cumulative addition method, the calculation of an arbitrary polynomial expression is sequentially performed on the equally spaced discrete values of the variable. First, the principle will be described.

 Now prepare N + 1 registers R 0, R 1, "-RN.

(OiV.PI An initial value κ is given to each of the registers. The contents of each register when the operation described below is repeated k times for each of these registers (this state is called the k-th step). The numerical values stored in the star are represented as (RO) _k , (R l) _k , (R 2) _k ,…, (RN) _k , respectively. Here, k = 0 corresponds to the case where this operation has never been performed. That is (R 0) ₀ = i ₀ ,

(R 1) ₀ = i ₁ ,…, (RN) ₀ = i _N. The above-mentioned operation applied to registers R 0 to RN is the cumulative addition as shown below.

That is, R 0 is the force to maintain the initial value i _Q ; the other vectors are the numbers of the previous step to the value of their own register of the immediately preceding step. The value obtained by adding the value of one register and the value of one register is added. The value of each register is of course determined by the initial values i ₀ , i ₁ , i _N and the number of steps k. This condition is shown in Table 1.

OMPI First

Next, given by the above method: The value of the given polynomial of degree N // ( _X ) is a discrete variable x = k X (k = 0, 1, 2, ..., X is the calculation interval) The method of sequential calculation by N-stage cumulative addition will be explained. The Nth-order polynomial given here that should be calculated is as shown in the following equation.

However, in the present invention, (5) is defined as a polynomial of X from / (X) = a ₀ + a _{l 3} c corresponding to N = 1.

 / (x) = + a X + a + N

+ ^a N ^X (5)

Considering the value of each register in the n-th step in Table 1 as a function of n, (R 0) _n is _n ^D , (R l) _n is n ¹ , (! ^ ? ^ Is n ² , (R 3) _n is n ³ ... (RN) _n includes n ^N terms, and (RN) _n = i _N + (^) Ϊ Ν-τ + (9 ) + -... '+

(? _τ ) i ο, / (x)

N is the Nth degree polynomial of n, so that (RN) _n is N + 1 unknowns i

It is a polynomial of degree N with respect to the variable n containing i _N , and therefore computes this polynomial if N + 1 initial values satisfying (RN) _N = / (nX) are found. You can One way x = n X

Substituting into Eq. (5), Eq. (6) is obtained.

 N N

(nX) = a _g + _ai Xn + a ₂ ^ n ^ 4- a _z ⁰ n ⁵ +… "-+ a _Ν " η

 (6)

In order for (RN) _n and / (n X) to be unequal, i.e., for all n = 0, 1, 2, 2, ... Therefore, the condition that the coefficients of both n ^k Γ k = 0, 2… N) are not equal to each other is necessary. (RN) _n is the variable n

O.V.PI

-:: 1 WiFO As a notational expression, it is shown as in the equation (7)

(RN) _n = g ₀ (io, i ₁ ,… i _Νso + g (i ₀ , ii-i N) _N

+ g ₂ (i ₀ ,-i N) n ² + "-…

… "-+ SN (io ' ¹ 1… ¹ N ( ⁷ ) (S) and ( ⁷ ) and the coefficients of n are equal to each other.

The condition of Eq. (8) is obtained.

g _k (0 ,, ¹ 1…) = a _k ^k ― (8)

 (However, k = 0, 1, 2 N)

According to Eq. (8), i 0, i… i _N can be obtained as the functions of a ₀ , a… a _N and: X, and when this value is obtained, (RN) _{Since n} / (nX) is satisfied, it is clear that the multistage cumulative addition method of the present invention can successively calculate arbitrary polynomial expressions for equally spaced discrete variable values. It is

 As a concrete example, the value of the polynomial shown in Eq. (9) is set as k = 0, 1, 2,…, and the calculation is performed step by step for the variable x = k X. To do.

/ (x) one α — χ ^ό + β X (9)

 In the case of, since Ν = 3, the equations 0) and ^ are satisfied.

(R 3) _η = .η ⁵ + (-i ₀ n + (-2 3

η + i ₃ (Μ).

 Here, by equating the coefficients of Eq. (0) and E, we obtain (Eq.

OMPI

 Solving the equation for i 13, 3 yields ^

This $ expression i ₀ , i! If i, i ₂ and i ₃ are used as initial values and cumulative addition is performed, then equation (0) comes to ffi.

 Now let's give actual values to β and X and perform cumulative addition. If a, β, and X are real numbers, they are good, but to simplify the calculation, we set = 1, β = Q, and χ = ι.

From this equation 0) / (k) = k ³ (k = 0, 1, 2, 3, ...) should be obtained. According to the formula 6 = 6

= 0, and using these as the initial values for cumulative addition, the results shown in Table 2 are obtained. It is obvious from this that (R 3) = k ⁵ is obtained.

"BUREAU-po _t v, _y Table 2

Brief description of the drawings

 The figure shows a block diagram showing the configuration of an embodiment of the polynomial computing device of this invention, and Fig. 2 shows an example of a periodic function created by cumulative addition of this invention. Figure 3 shows that the periodic function of the continuous variable X approaches a sin function or a cosign 'function by cumulative addition, Fig. 4, Fig. 5, Fig. 8 Figures 9, 9 and 10 show examples of functions obtained by 2-step cumulative addition, and Figure 6 shows functions obtained by 2-step cumulative addition. Figures and 7 show the function obtained when the function of Figure 6 is interpolated linearly, and Figure 11 shows two functions of the function given in Figure 9. Figure 12 shows the waveforms obtained when calculated at different speeds, and Figures 12 and 11 show the waveforms obtained in Figure 9; The figure shows the waveforms obtained by correlating the same number of master clocks with each other, and the figure shows the waveform of each cumulative addition in the calculation of the function given in Fig. 9. Figure 2 shows the waveforms obtained when the masks are made to correspond to two different types of master blocks, and Figure 14 shows the modulation waveforms that undergo self-modulation. , 1st * i

f OMPI- Figures 16 and 16 show the waveforms obtained by the mod, Figure 17 shows the waveforms obtained by the P · mod modulation, and Figure 18 Figure is a block diagram showing the structure of an electronic musical instrument to which the invention is applied. Figure 19 is a block diagram showing the composition of the Modulo X counter. Figures and 21 are block diagrams showing the configuration of the control signal generator in Figure 18, and Figure 22 shows the configuration of the memory groups that give initial values and values. The block diagram shown in Fig. 23 is a block diagram showing the configuration of the engine port counter, and Fig. 24 is shown in Figs.

 Figure 2 1 Output timing diagram of circuit, Figure 25 is circuit diagram of modulated wave generator, Figure 26 is circuit diagram of modulated wave generator, and Figure 27 is Figure 2 Examples of waveforms obtained by the circuit in Fig. 6 and'timing diagram of the input signal, Fig. 28 shows the synthesis process of the musical tone waveform, and Fig. 29 shows two-stage cumulative addition. Fig. 30 shows the waveform of the amplitude obtained by Fig. 30, Fig. 30 shows the waveform of time-varying amplitude obtained by the two-stage cumulative addition, Figure 31 shows an example of a waveform with the waveform obtained by two-stage cumulative addition, and Figure 32 shows the pattern in Figure 18 '. '' Circuit diagram of the Deck mouth generator, Fig. 33 and Fig. 34 are the circuit diagram of the control part of the envelope generator in Fig. 18, Fig. 35. Figure 18 is the circuit diagram of the waveform generator of the envelope generator, Figure 36 is the circuit diagram of the multiplier in Figure 18, and Figure 37 is the P-mode F-variable gjf. Figure 3.8 shows the obtained waveform, Figure 3.8 shows the waveform spectrum waveform of Figure 37, and Figure 39 shows the waveform waveform generator. Data R

OMPI Group, Figures 40 and 41 are circuit diagrams of the control section and waveform generation section of the full-time waveform generator, and Figure 42 is that of Figures 40 and 41. It is an example of the waveform obtained by the circuit and a timing diagram of the input signal.

 BEST MODE FOR CARRYING OUT THE INVENTION

The embodiment of the device for calculating a polynomial by this cumulative addition method has the basic configuration shown in Fig. 1 and has N + 1 registers R 0, R 1, R 2 In addition to R 0 of RN, the contents of the register at the previous stage and the contents of the register at that stage are added by adders 3 · ι, 3 ₂ … 3 _N , respectively. , Respectively, via _selectors 4, 4 ₂ ··· 4 _Ν . _Memories 2 ₀ to 2 _N are for storing the initial values io to i _N given to registers H 0 to 'RN at the beginning of the execution of cumulative addition in Eq. (4). R. In addition, the memory ₂ corresponding to each selector 4, 4 ₂ ... 4 _N. , The contents of the 2 ₁ ~ 2 _N are configured to cormorants'm given. In addition, the contents of _memory 2 _Π are directly given to R 0;

Control unit 1 is al provided here or we each Note Li 20, 2 ₁ ... 2 in _Ν Note Re A de Re scan signals, each Selector Address one 4, 4 ₂ ... 4 _Ν Is a select signal, and each register ϋ 0, R 1 ... RN is a latch signal. The output of the stage Ι 's rst RN is given to the display device 6 so that the cumulative addition value can be displayed. Register R 1 ~! IN — Any output of 1 may be displayed on display device 6.

 The initial value is obtained by solving the simultaneous linear equations in Eq. (8), given the polynomial, (x) in Eq. (5), and the calculation interval X.

O PI It is. For each polynomial and each fm interval, the precalculated initial values i _Q , i ₁ i ₂ , ..., i _N are respectively assigned to the corresponding initial value memory 1 Store in 2 2 2 _N. The controller 1 sets the memory address (memory address) corresponding to the polynomial and the calculation interval to the initial value memory.

Send to 2 2 2, ..., 2 _N. That ’s why

2 2 2, ..., 2 _N are the respective output terminals 1 0 ₀ ,

Outputs initial values ί ₀ , i ₁ , i 2, ..., i _N corresponding to 1 0 ₁ , 1, 0 ₂ ..., 1 0 _N. The output side of the initial value Note Li one 2 ₀ is always connected to the re g Turn-5 _0, Note Li one? Roh ^ to the force side Selector Selector Address - 4-! Input side of the input side of the output side of the Note Li one 2 ₂ Selector Selector Address one 4 _2, as well as below, Note Li one 2 _N outgoing 'force side Selector Address one 4 _N each Selector Address simultaneously o controller 1 input respectively that are connected Ru gave Note Li one first ground to an initial value Note Li group of 1 to 4 4 4 and select signal 8 is turned "ON" to memory 2 2

 The output terminal of one of the corresponding selectors for the output of 1 2 1 2.

…, Output to 1 2 _Ν . Therefore, the initial values i _Q , i · !, i ₂ , ...., i. _N appear at the input terminal of each register _. This time the control unit 1 sends the latch signal to each register 1 via connection 9. Initial value depending on the latch signal

 Each N is a register 5 5

It will be latched to 5 _N.

 After latching the initial value to the register, the select signal 8 is turned "OFF" and the adder 3 is added to the register R1.

 Z 2 RtAiT · 'CMPI

- Calculator 3. Is connected to the register R 2 and the adder 3 _N is connected to the register RN through the selectors 4 4 4 _N , respectively. This state corresponds to the number of steps k = 0 in Table 1. The adder 3 and the resister R l, the adder 3 ₂ and the register R 2, ..., the adder 3 _N and the register RN respectively constitute a set of cumulative adders. To do. That is, the adder 3 obtains one of the two inputs from the register R 0 in the preceding stage and the second input from the register R 1 in the same stage. Get it. These two inputs are added by the adder 3! And are given to the input 1 2 ^ of the register 1 R 1 through the selector 1! R. When a latch signal arrives in this state, the output of adder 3 is latched to register R 1. The second stage cumulative adder, which is composed of the adder 3 ₂ and the register R 2, also has the output of the preceding register R 1 and its own register R. The output of 2 and the two are input, and the two are added by the adder 3 ₂ and latched to the register R 2. Similar operations are performed in the cumulative adders from the third stage to the Nth stage. This state corresponds to the number of steps k = 1 in Table 1.

 Each time a latch signal arrives, the accumulator repeats the same operation and executes cumulative addition corresponding to the number of steps k = 2, 3, 4, 1, n. Thus, for a step number k = ii, the function value / (nX) is latched to the register RN, and the output of the register RN is Connect to the Ray device 6. As the display device 6, various devices are used depending on the purpose. Visually calculate the function value calculated sequentially

OMPI Is displayed on the screen, a CRT display device is installed, a printer is installed on the screen if printing is required, and a D / A conversion is executed if a voltage level is required. Used by container

The controller 1 and the initial values MEMO 2 2,, 2 '..., 2 _N serve as one function of the initial values i _a ,, ..., i N, so that 0 i fc: o This part is replaced by a computer that can solve the simultaneous linear equations of Eq. (8) with an initial value N, and the initial values are set to the registers R 0 to RN by that computer. You can also do

 Although the calculation of polynomials by cumulative addition performed in this way is limited to the sequential calculation of discrete equidistant variable values, For the calculation of polynomials, it is possible to simplify the calculation, which does not require complicated multiplication and only needs to give an initial value to perform cumulative addition. Since the calculation of the elementary function can be expanded by polynomial approximation and can be operated, it has the advantage that it is extremely wide in applications.

 Next, let us consider the calculation method of the periodic function as an example of applying the multi-step cumulative addition method. Usually, in the calculation of a periodic function, one period is set as a large section, and this is divided into several sections, and the periodic function is approximated to a polynomial for each section. It is. If the multi-step cumulative addition method according to the present invention is used, the initial value is calculated for each interval and cumulative addition is performed.

However, all initial values are calculated for each interval. Although this requires a large number of calculations, if the periodic function can be calculated without taking this overshoot, the calculation procedure will be further simplified. From this point, the initial value is not algebraic, and if there is a periodic function that can be calculated by simply changing the sign for each section, it is useful.

Now, let us consider the function (RN) _k of the number k of steps obtained by the multi-stage cumulative addition as shown in Table 5. In the device shown in Fig. 1, only the registers R 0 to R 4 are provided for the registers, and the initial values are set to R 1 to R 4 (R l ) ₀ = 0, (R 2) ₀ -=-8,, (R 3) ₀ = 8, and (R 4) ₀ = 4 6 are given respectively. As shown in Table 5, the contents of register R 0 (R 0) are '+ 1'at step 0 to 3 and 12 to 15 and L 4 at step 1 ~; L 1 To operate as 1. After Steps 16 and 16, repeat the operations from Steps 0 to 15. In other words, the content (R 0) _k of the register R 0 can be regarded as a function of the number k of steps, and is a function with a period of 16 steps. When the device shown in Fig. 1 is driven based on the above rules and cumulative addition is performed, the values (R 0) to (R 4) of each register R 0 to R 4 become the third value. As shown in the table.

ΟΛ'.ΡΙ IPO " OP-1M Table 3 Ό 1 Z ``

 0 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1

 κυ I 1

丄 丄 ― 丄 ― 1 —1 one 1 —1 ”one one 1 one 1 1 1 1 1 1 1 1 K1 _k Λ

 U bowl o 4 1 0 —1 —2 —3 —4 one 3 —2 one 1 0 1 2

— 7 ― c ― ο

 No k O Q o ― O 0 v o Q Q n r

 o (r

 0 Z 0 one o o o one 7

(R3) _k 8 0 one 8 one 15 -20 -22 one 20 -15 —8 0 8 15 20 22 20 15 8 0 one 8

(R4) _k 46 54 54 46 31 11 1 11 -31 -46 -54 1 54 -46 -31 -11 11 31 46 54 54

Observing Table 3 _reveals the following: o (R l) ₀ = (R l) "i ₆ , (R 2). = (R 2) _{1 ό} , (R 3) = (R 3) _{1 6} ,

Since 4) ₀ = (R 4) ·! _6, (R l) _k , (R 2) _k , (R 3) _k , (R 4) _k are the same as (R 0) _k 1 6 It is a function whose period is the step. Figure 2 is obtained by plotting (R 0) _k to (R 4) _k as a function of the number of steps k. The amplitude axes are appropriately scaled for ease of comparison in each draft in Fig. 2. Looking at this figure, as the number of stages of cumulative addition, immediately (1: ^] ^, increases, the waveform gradually approaches the sin 'function or cosine function. You can see how they are going.

 The amount of harmonic distortion of the periodic function obtained as the number N of cumulative additions is increased is reduced in the following consideration. Generally, DC is included with a period of 2

 ∞

The non-function Ba x) is Ba) = ∑ a _k sm (k _x + i5 _k ). The periodic function g (x) obtained by integrating this function is =

cos (k _x +? 5 ,,) + c. Function here

Assuming that the harmonic distortions of / (x) and are d _f and d _g , respectively, the harmonic distortion ratio d _g Zdf is as follows.

OMPI

-^ Look 0 2

a 1 In particular, if you want to include even-order harmonics, the following equation holds from a ₂ == a ₄ a ₆ =… = 0.

3

The cumulative addition method, which is equivalent to the quadrature method, is almost equivalent to integration. Therefore, the harmonic distortion of the periodic function (RN + 1) _k , which is obtained by cumulatively adding the periodic function (RN) _k with no DC component, decreases as explained above in comparison with (RN) _k .

The initial value given to each register in Table 3 is given as the DC component is generated by cumulative addition. In this case, the functions of (R0) _k to (R4) _k have even-order harmonic components, which is obvious from the symmetry of the function. The amount of distortion is almost · ¾ (-9.54 dB).

o.vipi Table 3 shows the function (RN) _k with 16 steps as the period-, but the number of steps may be smaller or larger than 1-6. Gives a similar function. For example, a similar religious church (RN) _k with a period of 4 II states ° is k = 0 to n — 1 (E.0) _k = 1,, k = i! ~ 3 n — 1 with (R 0) _k = — 1, k = 3 I! We set (R0) _k = l for ~ 4 π — 1 (repeating from k == 0 after k = 4 n), and the initial value is (R 1) Q = 0, (R 2 ) o = one (R 3) n = (R4) n

2 ⁿ = 2 ⁿ 24

(5 n ² -l 1),…, is obtained by performing cumulative addition. As a matter of course, the quadrature method approaches the integral more and more as the number of steps included in one cycle increases, so the above discussion on harmonic distortion is quantitative. It will be gradually accurate.

 Here, we obtain the harmonic distortion of the periodic function (RN) obtained by cumulative addition when the number of steps included in the period is infinite.

 Since cumulative addition with an infinite number of steps is equivalent to integration, the function in Fig. 2 when the number of steps is infinite has a step number k of continuous variable. It can be obtained by substituting for X and using the function similar to that in Fig. 2A as the starting point and integrating it one after another.

 The function corresponding to Fig. 2A is the function with period 2 in Fig. 3A. By successively integrating these, the functions of B, C, and D in Fig. 3 are obtained. The integration constant that occurs after integration is chosen so that the DC component of the obtained periodic function is zero. In addition, the maximum value of the amplitude of the function is standardized to ± 1. in this way

C.'uPI w ^ifj o If the obtained functions are / ο χ) (x), f ₂ (x), and 3 (x), then the respective functions are expressed as follows. Na / ₀ (x) is shown in Fig. 3A, and (X) is shown in Fig. 3B-respectively.

, Ku)

The Fourier expansion of these functions may be calculated directly, but since the two adjacent functions are integral and integrable with each other, the first one / (3 If (Χ) is found, the other functions can be found by successive integration, and ₀ (X) is a rectangular function, which can be expanded to a Fourier ヱ as follows.

 1

n 0 (x Λ) -No — _π (C ι0κSX on — g'c ⁰⁵ ^ ^x + "cos ox cos 7 x H) So the other functions are as follows.

 8 1

) = — ( ^Sin X sin sin 7x ten…)

 96 1 1 1

 z (x) = —- ι, sin x; sin3x + — sin5x: sin 7 x ^ j

ό π · 4 3 54 7 When the harmonic distortion of the function _π η (χ) obtained by successive integration is represented by d _n , the following equation is obtained.

½

 d = (—— -— + ,,

n, 2n + 2 5 ² ^ + 2 + γ 2 η + 2 +…) These results are shown in Table 4. D in the table

, Are functions included in one cycle of functions (R 0) _k , (R l) _k , (R 2) _k , (R 3) _k ,…, which are similar to the waveforms shown in Fig. 2. It corresponds to harmonic distortion when the number of taps is set to infinity. Fourth clothing harmonic distortion (° h)

4 8. 3 4 2 6

 1 2. 1 1 5 3

3.8 0 4 1

 1. 2 4 5 7

0.4 1 2 8 d ₅ 0.1 3 7 3 d6 0.0 4 5 7

 0.0 1 5 2

 0.0 0 5 1

ΟΜΡΙ Next, let us look at what kind of curve the periodic function (β N) _k obtained by T is multiplied by the cumulative addition shown in Table 3. As already mentioned, any N-th degree polynomial can be calculated by N-stage cumulative addition. In this case, the coefficients a ₀ , _{& 1} , a 2, ..., a _{N of the} polynomial and the calculation interval X are given, so i ₁ , i ₂ , ..., i _N are set as unknowns and simultaneous It suffices to solve the linear equation (8). Conversely, given the initial values i 0 ,, i ₂ ,…, i _N and the calculation interval X of cumulative addition as shown in Table 3, the simultaneous linear equations (8) can be expressed as a Q, _{& 1} , a 2, If we solve for A _N, we obtain a polynomial that passes through the function value (β N) _k .

 Here, as an example, as shown in Table 3, (R 0) is n + 1 and 2 n 1 1, n + 1 and (R l). =

0, (R 2) _a = — · To obtain a quadratic expression that passes through the periodic function (R 2) _k obtained by two-stage cumulative addition, with the initial value of _η ² .

The periodic function (R 2) _k consists of the cumulative addition of three parts with different initial values. Therefore, there are three quadratic equations corresponding to the three parts. The first one goes through (R 2) Q ~ (12) ^;!, The second one goes through R 2) _n ~ (R 2) _5n —, and the third one goes (R 2) _3n to (R 2) _4n —. The first one also goes through (R 2) _n . This is because the value of (R 2) _n is determined regardless of the value of (R 0) _n . Similarly, the second one goes through (R 2) _3n and the third one goes through (R 2) _4n . Therefore, the three quadratic equations to be obtained therefore pass through (R 2) to (R 2) _n, and (R 2) It passes through (R 2) _3n, but it passes through (R 2) _{3n + 1} ― '(R 2) _4n 0

The origin is located at step k = l, and the number of steps in one cycle 4 n is 2? Corresponding to Γ (meaning that X in Eq. (8) is set to ^ "), the quadratic equation obtained by normalizing the maximum value of the amplitude to ± 1 is _g (x ), The following formula is obtained.

g _{(χ) =} ― _{(: χ} — "(— _{3) +} ('π, Ζ ^

1, 2

(fx-3) (fx-5)-(-^), ₂ : π. <χ <2 π Therefore, if the step number 4 II in one period becomes infinite, the function g (x) It is clear that is consistent with the above-mentioned function / ₂ (χ) .The function (R 0) _{k that} is cumulatively added first is as shown in Table 5 and Figure 2A. It was a function of different sign type. However, it is good that this function is not a cosign type. For example, even if the sine type is as shown in Table 5, it is possible to approximate the sine (or cosine) function by cumulative addition. In this case, (R 0) is k = 0 to 2 n — 1 and ^ ■ 1, k = 2 I! ~ 4 n — 1 + 1, and initial value (R 1) ₀ = n, (R 2) ₀ = — 7 n, (R 3) ₀ = 2 "n —-^ n ⁵ ,, (R 4) ₀ = ^— N + ^ n ³ , ―. The case of η = 4 is shown in Table 5. It is clear that this is compared with the case of Table 3. The functions (RN) _{k in} Tables 3 and 5 are exactly the same function, and the only difference is that the phase (the position of the step that gives the same function value) is shifted. is there .

 OMPI

W1PO _<¾ In the above explanation, both the sin type and the sin type have 4 n (= 1, 2,3,4, '...) as one cycle. In the case of the in type, 2 n (n = 1, 2, 3, 4, ...) can be set as one cycle, and (R 0) _k is k = 0 n 1 1 and 1 1, k = n ~ 2 n — 1 with +1 and also

(R 2) _n = n

0 = 2 ⁿ 4 ⁿ ' ^{(R 3)} o ⁼ 6 ^{n _} 2

 (R 4) n,

— 8 ^{n +} 16

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n00 / 6 £ Jf / 13d 99IS0 / 08 OAt In the above, for example, we described how to create an approximate sign (or cosign) function by cumulative addition as shown in Table 3. Therefore, the number of stages of cumulative addition is increased and the number of steps included in one cycle is increased, so that the accuracy is high and the sign (or sign) is high. We have shown that the function is calculated. At the same time, the trail of addition points obtained by two-stage cumulative addition is given by a combination of quadratic functions, and thus it is shown that a sufficient function is given.

 'Next, we will explain various other functions that can be created by using two-stage cumulative addition. The cumulative addition in Table 3 is'

The initial values were given as (R 1) ₀ , (R 2) ₀ , (R 3) ₀ , and (R 4) _0, and the sign of (R 0) _k was controlled. Next, we give an initial value as T, (R 1) _0,. (R 2) ₀ , (R 3) ₀ , (R 4) ₀ , which is similar to this, and ) Take up the two-step cumulative addition that controls the absolute value and sign of _k . One of them is shown in Table.6.

In this case as well, see Fig. 1 for register R 1 ~! The initial value of (R 1) ₀ = (R 2) ₀ = 0 is given to I 2, and the value of (R 0) is + 4 and k = 4 ~ at steps k = 0 to 3. l 1 is one, k = 12 to 15 is +4, k = 16 to 19 is +2, k = 20 to 27 is one 2, k = 28 to 31 is +2, When k = 3 2 to 3 5 + 1, 1 at k = 3 6 to 4 3 + 1, at k = 4 4 to 4 7 + 1 k = 4 8 and subsequent values k = 0 to 4 7 are repeated. Give and give 0

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As shown in Table 6, (R 0) Q = (R 0) _{4 8} and (R 1) ₀ = (R 1) _{4 8} and (R 2) ₀ = (R 2) _{4 8} results are obtained, and if (R 1) _k and (R 2) _k, k = 0 to 4 7 is a periodic function with one period. . Figure 4 shows (R 2) _k as a function of k. Here, the absolute value of (R 0) _k , that is, 4 for k = 0 to l 5, 2 for k = l 6 to 31 and 1 for k = 3 2 to 4 7, is the approximate cos "Ha. Scale in proportion to the maximum amplitude of the loose. By the way, one cycle is a function with 4 ιχ steps, and at steps k 2 0 to n — 1, (R 0) _k = + c, k

= I! At ~ 3 n — 1 at (R 0),-= — c, ¾: = 3 ~ 4 at 1

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99IS0 / 08 OA As a second example, let us describe .2 stages of cumulative addition as shown in Table 7. (R 0) _k is +1 at k = 0 to 3, 1 at k = 4 to 7, 1 at k = l 6 to 19 and 1 at k = 20 to 24, +1 and k = 8, 9 = 1, k = l 0 to 1 3 +1, ^ = 1 4, 1 5 gives a value of 1 and = 2 4 and later, even if k = 0. The same value shall be repeated and given. The initial values (R 1) _Q and (R 2) ₀ are 0. The value of the periodic function of (R 2) _k obtained by this two-stage cumulative addition is as shown in Fig. 5.

As shown in the first and second examples, the initial value (Rl) is obtained by cumulative addition in two stages. , (R 2) _Q, and by controlling the absolute value of the value given to (R 0) _k and the sign, it is clear that various periodic 'functions can be obtained. Is.

 In addition, the cumulative addition method has an advantage that the value of the polynomial between adjacent steps can be approximated by the linear interpolation method (linear interpolati on). As already explained, an arbitrary polynomial f) can be calculated for X = k X by the cumulative addition method. Suna Echi /! ^ Ni! ^: ^, ((K + l) X)

= (RN) _{k + 1} . When the calculation interval X is divided into

 The value of ((k +) X) (ι η = 0, 1, 2, 3, 3, ···, ^ — 1) is as shown in the following formula by the straight-line approximation.

((k + f) Χ) ~ (RN) _k + {(RN) _{k + 1} — (RN) _k g "" ... 4 From equation (4), (RN) _{k + 1} ― (RN) _k two (RN — 1) Since _k is substituted into equation ^, the following equation is obtained.

((k + |) X) ~ (RN) _k + (RN-1) _k $ The right-hand side of equation ^ is the value of the Nth register T ~ R .N at the kth step (RN), and the N — 1st register RN — 1 of value in the k-th scan STEP (RN - 1) divided by the value out of the _k (RN- 1) _k a m times Tsu by the and the child you cumulative addition obtained et al is Ru. That is,

If (RN-1) _k and (RN) _k are used as initial values, then N-th stage cumulative addition only needs to be performed m times. If o is chosen to be a power of 2 ;!

The calculation of (RN — 1) _{k is} a shift operation.

When calculating the function value for an arbitrary value of the variable _X like this, the calculation interval X is initially large, and then the calculation interval is small.

Cumulative addition o

 Therefore, the approximate calculation of the numerical value / ((k +) X) can be performed by cumulative addition of k + m steps. The first advantage of using linear interpolation for polynomial calculation is that it can increase the speed of calculation. The second advantage is that it saves the number of guest bits used for cumulative addition.

 Even if the function values are desired one after another, as in the case where the graphs are displayed in the graph tube by graphics (graphi cs), the straight-inner method is adopted. You can In this case, it is possible to take advantage of the second advantage mentioned above. In this case, ^ is adopted as the calculation interval from the beginning, and the value on the right side of the equation is sequentially obtained by cumulative addition. That is, all k (k = 0, 1, 2, 3, 1, 1) on the right-hand side of the equation and all m (m

= 0, 1, 2, 3, 3,-, ^-1) is calculated sequentially by accumulative addition at this calculation interval. Write the value of the register as (R n) _k , _m (η = '0 1., 2,-' ·, Ν), which is the register R n ( n = 0, 1, 2, 2, ..., Ν) is defined as the value at the (k + m) th step. Let's look for (RN) _m ^_ that satisfies the ^ equation by cumulative addition.

(RN) '.k, m = ( ^RN ) k + ( ^RN — 丄 ノ) _k …… It is given as the initial value of.

(R n) _{0> 0} = J (R n) _n , n = 0, 1, 2, ..., N '

 }

(R) _{0) 0} = (RN) ₀ or the cumulative addition to the register R n (n = 1, 2, ..., N l) is the k-th (k = 1, 2, 3, 2,…) The desired result can be obtained by performing the steps intermittently and performing cumulative addition to the register RN for each step.

 Cumulative addition to the register R n (n = l, 2 ·····, N — 1) is performed only when m = 0, and the following formula holds. , 2,-, -N-1 ... one

In addition, the definition of cumulative addition (Equation ( ⁴ )) generally yields Equation ( ⁹ ).

(RN) _k = (R ^ j ^. ^ 4- (R N- l) _k _ ₁

= (RN) _k _ ₂ + (R N- l) _k _ ₂ + (R N- l) _k _ ₁

= (RN) _k _ ₅ + (R N- l) _k _ ₃ + (RN-l) _k _ ₂ -f (Ri ^ -l) _k _ ₁ ..

= (RN) ₀ + (R1SF-1) ₀ + (Rl ^ -l) ₁ + (RN-1) ₂ -I— ^ (ΚΝ-Ι) ^

Therefore, from Eq. (19), Eq. (19) is obtained p

(RN) _k- m _ni = (RN)

0, 0 RN- L ', q +' ¹ (RN-i)

pp == 0 ° qq = 0 q two 0 (RN-l) _k

 K

 k one 1

= (RN) ₀ + ∑ (RN-1) + (RN— 1) _k

 p = 0

= (RN) _k + (RN-1) _k ^ O) where 0 = 1 _} in Eq. 0) β = Q, and the function shown in Table 2 is obtained when X = 1. Perform a straight-line interpolation calculation of the value (R 3) _k . = 4 gives the results shown in Table 8 when it is directly interpolated and X = X.

 Also, when α = 1 and ^ = 0 in Eq. (0), the exact value of the function is calculated when the direct injection is not performed when X = X.

The calculation of (R 3) is performed by giving the initial values i _Q = 6 64, i = 6/6 4, i ₂ = 1/6 4, i ₃ = 0 by the equation ^. It is. The results are shown in Table 4. Looking at Tables 8 and 9-41, it is natural that (H 3) 4 _k = (R 3) _k n = (R 3) _k holds. It is bright. ヽ ヽ

Table 8

4 k + m 0 2 3 4 5 7 8 9 10 11 12 13 14 15 16 km 0,0 0 ,: 0,2 0,3, 0 1,1, 2, 3 2,0 2, 2,2 2 , 3 3,0 3 ,: 3,2 3,3 4,0

(R0) _k , me / Q 4 ^ 4 6 ^ 4

( ^R l) k, m $ / 4 1 1 4 24/41 3 (4 ( ^R 2) _k , _m 4 7/4 19/4 37/4 6 Χ

( ^R 3) _k , _m 1/4 24 y {4/4 11/418 / 51/470/4 89 / 410fH 145

(R3) _k 0 1 8 27 64

Table 9

Table (8) and (R3) _km . Table 9: When comparing the numerator of the value of-in the same step of R3 (the denominator can be calculated by the shift operation). ) And (R 3) are larger than (R 3) _k and _m . In order to calculate an accurate value, it is necessary to increase the number of bits (bits) in one register than to calculate by the straight-line inward method. There is an advantage to using the direct hoisting method in this case.

The following is an example of applying this Naoki Honai method to a periodic function. Table 10 with the period of 8 steps obtained by 2-step cumulative addition is shown in Table 10 and the function with a waveform as shown in Fig. Is applied. If ^ = 4, the initial values (R 1) ₀ , 0, (R 2) 0, 0 and (R 0) _k , _m are set as shown in Table 11 and the function is We get (R 2) _{k> m} . This is shown in the waveform of the real gun in Fig. 7. In Fig. 7, the function of Fig. 6 is also multiplied by 4 times the number of steps and immediately by 4 times on the horizontal axis. The stretched state is shown in breaches.

As already mentioned, one of the advantages of using the linear interpolation method is that the number of bits (bits) in the register is small. In the case of dividing each step by ^ with a two-stage cumulative addition similar to Table 10 of one cycle of 4 n steps, and squeezing in a straight hole, one cycle of 4 n The number of bits of the register R 2 is ^ compared with the case where it is not directly attached to the step. g ₂ bits small but small

Hi 4 Table 10 k 0 1 2 3 4-5 6 7 8

(R0) _k 1 1-1-1-1 -1 1 1 1

(R l) _k 0 1 2 1 0-1 -2 1 0

(R2) _k 0 0 1 3 4 4 3 1 0

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: '― ΟΛΙΡΙ y. W1P0 λ. Ϊ́Ο Next, in the cumulative addition method of the present invention, the multi-stage cumulative addition is defined by the formula (4) which explains the shape and formality.

 It is a hoop type for N. The hoop type means that the function of the sum of initial values of is the sum of the set of initial value functions and another set of initial value functions.

'That is, if the two initial values are (i ₀ , Ϊ ₁ , i ₂ , ..., i _N ), (j 0, j ₁ , j ₂ , ..., j _N ) To establish .

(RN) _k (i o + j ο, ii, i 2 + i 2 '…,

= (RN) _k (i 0, ii, i ₂ , i, i, _N ) + () _k (jo, ji, j 2, ...., where (Rl kCi ^ ii ^…, i _N ) is Initial value is i Q 'i

i ₂ , ..., i _N are the values at the k-th step of the _Nth register by multi-stage cumulative addition. The same applies to the initial values ^, ... 3 N. This is also clear from Table 1. This is because (RN) _k (io, i 1, i 2, ..., i _Ν ) is a linear combination of i ο, i, "i u,…, i _Ν . Therefore, when calculating the sum of two functions according to the present invention, it is possible to calculate the sum of the initial values by giving the sum of the initial values. become .

An example of application of this principle will be described. Table 10 shows two-stage cumulative addition with initial values of (R1) 0 = (R2) 0 = 0. Here, (R0) _k changes with the value of 4, 1 4, 0, as shown in Table 1 2. The (: R2) _k obtained from this is as shown in Fig. 8. Similar examples are given as different functions in Tables 13 and '9. In this case Fig. 8

· "OXPI

\ WiPO t When the sum of the function shown in Fig. 9 and the function shown in Fig. 9 is calculated, it is not necessary to make a cumulative addition for each function to form the sum. Using the properties of the cumulative addition method described above, it is desirable to perform cumulative addition with the initial value of the sum of the initial values.

The situation is shown in Table 14 and Figure 10. (Rl) o, (R2) ₀ , (R0) _k in Table 14 are the sums of the corresponding ones in Tables 12 and 13 respectively. The function (R2) _k created in this way is as shown in Fig. 10, but it is clearly the sum of the functions in Figs. 8 and 9. Reply

——OMPI.

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99 0/08 OA In the above, we have explained by taking the functions of the step variable k and the misread variable X which are divergent when calculating the polynomial: formula by cumulative addition. These will be described when they are applied to the formation of waveforms that are generally a function of time, such as musical tone waveforms.

The function with the waveform t, which is a function of time, as the variable, is obtained by the difference between the scattered step variable k and the continuous variable _X with the time t. Get Therefore, various waveforms can be obtained depending on the difference between k and the time t.

The waveforms shown in Figs. 2, 4, 5, 8, 9 and 10 described above are all functions of the number k of steps, and the cumulative addition of each step is performed. If is executed for a fixed time t ', the respective waveforms are obtained. In this case, if the variable X is related to -time t and the hull form and is given as _X = t (or a constant), then waveforms similar to each are obtained.

 Now, let's consider what kind of waveform can be obtained by changing the relationship between the step variable k and the time t.

For example, when creating a function with a waveform such as that shown in Figure 9, at steps k = 0 to 7, each step is calculated at time interval 2: and step k = 8 In ~ 15, each step is calculated and viewed at time intervals. The waveform (R2) _t obtained in this way is as shown in Fig. 11 1.

As shown in this example, the shape of the function waveform is determined by the relationship between the step variable k and the time t. At the same time If, change the frequency of its' and this you ^-: there Ru. This is particularly important when forming musical tone waveforms, and since musical tones have a certain number of intervals determined by their pitch, this step. There is a limit to the way the relation between the time t and the time t, and it is not possible to make arbitrary relations.

 Also, the frequency required to form a musical tone waveform covers a wide range, but it is not necessary for this to be completely continuously variable, and it is sufficient if it has a predetermined resolution. .. Therefore, it is possible to use discrete discrete frequencies by associating with discrete variables in cumulative addition. As a means of giving such a scrambled frequency, there is a module X method (mo d u l o -X m et h o d). This is also called the frequency division method. The frequency master clock is counted at the X-adic count and the synchronization signal is obtained at every one buff. This is a method of forming a repeating waveform in synchronization with the synchronization signal of σ

 In the case of, the interval between adjacent sync signals is, and so the repeated waveform has a frequency of and the frequency obtained by the modulo X method is (X 1, 2, 3…), which is an integral fraction of the frequency of the master mouth.

 Therefore, if f is set to a sufficiently large value, the frequency resolution will be improved. However, a frequency of about 2 MHz is sufficient for the synthesis of a musical tone waveform. Say

That is, a periodic waveform of .125 500 Hz is obtained. Here, the method of applying various types of waveforms by applying the modular: cumulative addition to the X method will be described.

Let us assume that the number of mask mouths is 1600, and we divide these into m steps, and each step has r _k , (k = 0, 1, 2 ... m — 1) to include the master block. In this way, the shape of the obtained waveform is determined by m and r.

In this case, m and r _k are given the following formula.

 m-1

∑ r _k 6 0 0 For example, m = 16 and ro = r ₁ = r ₂ = r _{1 5} = l 0 0, and the master clock frequency is 2 MHz. By performing the cumulative addition as shown in Table 13 above for each step, the function of the waveform as shown in Fig. 12 at the frequency of 125 Hz can be obtained. Can be done. In this case, by changing the condition between m and r _k ,

50,

_{T'Q - τ '9 = = 5} 0 and I is' 1 2 5 0 Hz of the functions of the Let's Do waveform shown in the first 3 Figure that having a frequency obtained Ru this and can. Figure 12 and — Horizontal in Figure 13 shows the number of clocks ^, which is related to time t and t = ((= 0.5 A se c)). ..

 The method of creating the waveform shown in Fig. 13 from the waveform shown in Fig. 12 is referred to as modular X modulation.

 m-1 m-i m-1

In this case = r _k + q _k ∑ ∑ + ∑ q. .V.PJ m-1 m-1

And ∑ r'k = ∑ r _k = 1 6 0..0, so the following equation holds. M-1

Σ q _k ^{= 0} q _k the modulation sequence and call q _k = F _M the modulation function at the time of the I * F _M, you in and hump modulation index and call 'the I. In the above example, the function (R2) _{k in} Table 13 is called the modulated function F _c, and the waveform in Fig. 12 is called the modulated waveform and its frequency is indicated by c. The waveform in Fig. 13 obtained by modulation is called the modulated waveform. Also, when (R0) _{k in} Table 5 is used as a modulation function, the timing that generates the modulation sequence q does not correspond to each step in Figure 13. Therefore, the modulation function itself will also be subject to modulation. This is called self-modulation and the waveform obtained by this is called the modulation waveform, and its frequency is represented by m. The modulation function of Table 5

When (R0) _k is used and I = 1 50, the modulation waveform is as shown in Fig. 14 below. Below are some examples of the waveforms of the functions obtained by Modulo X modulation. In all of these examples, a periodic function of 1 2 5 O Hz that returns the same waveform every 1600 clocks at 2 MHz is created. In the calculation of the waveform, the 2-step cumulative addition of 16 steps is used, and in the unmodulated bark with modulation index 1 = '0, the f-calculation of each step is 10 0 black

, Λ I will do it every day. Immediately ~ _k = 1 0 0 (k 0,

2 5) No.

Table 15

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 k 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

F

 -8 —8 — 7 —5 1 2 2 5 7 8 8 7 5 2 -2 —5 —7

One 80 One 80 -70 -50 -20 20 50 70 80 80 70 50 20 —20 -50 -70

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

20 20 30 50 80 120 150 170 180 180 170 150 120 80 50 30

20 40 70 12C 200 320 470 640 820 1000 1170 132C 1440 1520 1570 1600

0 0 1 3 6 10 13 15 16 16 15 13 10 6 3 1

The example of the first waveform has various values as shown in Table 15 and therefore, (R2) _k shown in Table 3 is used as the modulation function F _M , and the modulation index Let I = 10 and use (R2) _{k in} Table 13 as the iron modulation function F _c . This waveform has a shape as shown in Fig.15.

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' Table 1 6 Table k 0 1 2 3 4 5 6 7 8 9 10 11 1

(R0) _k 1 1 one one one one one 1 —1 1 1 1 1 one one one one one

(I ") _k 0 1 2 1 0 -1 single 2 -1 0 1 2 1 0

(R2) _k 1 2 — 2 — 1 1 2 2 1--1 -2 -2 — 1 1 2

An example of the second waveform is shown in Tables 1–6 . ^: Each such step is used with a function (R 2) _k that has eight such steps as the period (R 2) _k. Diff. The frequency m force of the modulation-waveform, which is obtained by dividing 1100 clocks π ck, is 2500 Hz. This place

5 If the combined modulation index 1 = 40 and the (R 2) _k shown in Table 13 as the modulated function is used, each value of the waveform is as shown in Table 17 The waveform as shown in Fig. 16 is obtained. Since the frequency of the modulated iron c = 1 250 Hz, this waveform has fz / T m =. This waveform contains only odd-numbered overtones or zeros. So far, the modulation function has been used as the modulation function, which is obtained by cumulative addition. However, for the modulation function, the cumulative addition

• It is possible to use both non-arithmetic. For example, if the modulation function F _M shown in Table 18 is used and the modulation index is I = 5 50 and the iron metamorphosis is F c and (R 2) _k in Table 13 is used, The waveform as shown in Fig. 17 is obtained. This is what we call P mode modulation in the special case of modulo X modulation.

_ ΟΜΡΙ ―, W PO—

OMPI However, for example, in theory, the waveform that has undergone the module X modulation as shown in Fig. 15 and Fig. 1 is theoretically "4". Ο

In this case, for ease of discussion, the function with negative sign is used as the function and the function as sign is used as ^-9 O o This is because the periodic functions obtained by the multi-stage cumulative addition described so far give a sufficient approximation to the sin and cosine functions. The modulated waveform is obtained by calculating one cycle of the cosign function with a negative sign by N m step, and the modulated waveform is one of the sign function. It is obtained by calculating the local period with N c steps. Also, the master assigned to one step when no modulation is performed, and X is the number of clocks of the clock, and X is the variation waveform and the S variation droop shape. 0 ₀

 Then, at time t, the modulation waveform and the modulated dredge shape are calculated in the n-1st step. Up to n — 1 step k

 The number of master blocks

1. ∑ — 0 _Ί i ^J ) is given by the following equation. n-1 2 7 Γ

X _π n _- r T, cos (―— k)

 1 = 0 "I m Equation ^ is the local period of the masterpiece mouth is T 0

Since T o is equal, the equation is established. nr ¹ 2 Tt

n 1 1 1 COS ~ k no ^: „

1ί = 0 N m 丄 o N If the number is large, the following equation holds. n-1 2 π N m n-1 2 π; 2

 ∑ cos (k) = ∑ cos (': -k)

 k = 0 N m 2 π k = 0 N m N m n

Substituting this into the formula ^ and rearranging yields the following formula.

 m— esin $ 5 m = ym t ¾

2 π 2 7Z

However, e ψ m = η, Co HI C me ^) o

 X Nm XN m T o where m and ω m are the phase and angular frequency of the modulated waveform, respectively.

By solving the ^ formula according to the position of ^ m, the following formula is obtained. oo

<P m = cmt + 2 ∑ Jl (ke) sin (k ω _m t)

 k = 1 k where .J k (x) is the kth-order Bethel number of the 1st kind, o is the position and angle of the variable glazed type

* 1 out of 9

 Φ c = —— II and ω c = ——

N c X N c To obtained φ c = ω ct + 2 L — Jk (ke) sin ^ k iym t)

 N c k = l k-Therefore, the wave form subjected to the modulo X modulation is represented by the formula

Ό o

Nm ∞ 1

 sin0 c = sin {® c t + 2 2, — Jk ^ k e) sin (k cym t)}

 N c k = 1 k

 69)

ΌΜΡΙ

, WIPO A Also, it has undergone self-modulation-the modulation waveform is 00) and is expressed by the equation. cos ^ m = — cos {"ir 't + 2〉" one Jk ke sin (kmt)

 1 ^ = 1 k

 Therefore, the waveforms given by Eqs. (9) and () obtained by the modulo * X transformation are due to infinite term frequency modulation.

 1 ω c N m

The waveform takes various shapes according to e = — and —— = ——.

N m X ω m ΪΝ '

 If Ό o is a small ratio of the number of reeds, then

N c

 Ν m

Waveform becomes a harmonic dredge, and becomes a small integer ratio

 N c

If not present, an anharmonic waveform will result. The inharmonicity of such waveforms is especially noticeable in percussion instrument sounds such as drums and cymbals. Here, we will explain the multistage cumulative addition method of the present invention, which has been described above, and its principle device based on an example in which the tone generator is different. Figure 18 is a block diagram of a specific implementation key when this sound source ^ is applied to a tone generator. The cultivated urban area 14 collects information about the played construction board II. This information is coded with the KEY signal that becomes "1" when the board is misaligned and the code that belongs to the broom, 0 C (0, 1, 2,) , And a 4-bit signal TC (0, 3) that is a code of the 12 semitones (CCDD) in the octader. The control signal generator 15 has key sympathy 'W 1 4 to KEY, 0 C, T C, modulated wave generator 1 6 ^ to 20 bit

 G (0,… 19) is given as input. KEY signal

 U R Hi

O.P!

LV iP "0 Is placed underneath the key, and the logical value of the signal is "1" when the switch force is 0 N, and the keyboard returns to the switch. With the signal turned off, the logic value of the signal is "0".

 The 0 C signal is coded in the range of the tone equivalent to the fundamental tone, so it is coded by the control signal generator 15 and, for example, the 1st to 5th year groups. In the case of, it is output as a 3-bit code, depending on which pitch the talented club to which the sound belongs belongs to.

One octave contains 12 semitones, but the note names of C, H, A ~, '--..., C ~ are applied to it. The corresponding number of local waves is given in Table 19 and has a power of ⁵ , which is four times as many as! It is necessary to divide the required number of stages to obtain the desired frequency.

Table 19:

The T C signal is used to distinguish between these 12 tones, and the 4-bit tone name code (T C 0, T C 1, T C 2,

 T C 3). The correspondence between note names and note code is shown in Table 20. For example, if the clotted sound is, the note name code (T C 0, T C 1, C 2, T C 3) = "1001" will be applied.

0 MPI

, WiPO, Festival 2 0

Each S force of the signal control signal generator 15 is used by the modulation wave generator 16, the iron modulation wave generator 17 and the calculator 20.

Of the forces obtained from the relaxation signal generator 15 I (0 — 5) is given only to the irregularity generator 16 and OCT (1… 5), PSTP, P CYC, LDCYC _% WMCLK and PXOR 1 are given to the modulated wave generator 16 and the modulated wave generator 17 respectively. In addition, PXOR 2 and IHB are given to the iron modulation wave generator 17 and ET CK is given to the multiplier 20.

Ό The 6-bit I (0, '... 5) is the above-mentioned ^ variable index, and the 5-bit OCT (1, ... 5) signal is the special code OC (0 , 1, 2) are the signals obtained by decoding the same, and P STP is the signal synchronized with each step of cumulative addition, and PCYC is the approximate co-sign. The signal synchronized with the trailing edge of the pulse, LDCYC is the signal used for the initial value load, and WMCLK is the signal for P'type of the modulated wave generator 1 6 and the iron modulated wave generator 1 7. , RX0R1 and PXOR2 are signals for taking the number of 2, IHB is a signal for prohibiting cumulative addition, and ETC Κ is a multiplication signal.

 The modulation signal generator 16 receives the signals I, OCT, PSTP, PCYC, LDCYC, WMCLK and PXOS 1 from the control signal generator 15 and the modulation signal signal MG (0,…) of 20 bits. , 19) is generated. The modulated wave generator 1 7 is a modulated signal signal of the town control signal generator 1 2 and the signal OCT, PSTP, PCYC, LDCYC, WMCLK, PXOR1, PXOR2 and IH3. No. WG (0, ..., 11) is generated.

 In addition, the pattern'clock 'and the clock generator 1 8 are the master's clock MCLK and the waveform's rising and falling peaks depending on the division of MCLK. . The clock signal A3CLK: that determines the clock is sent to the π-pp generator 1 9.

 ARCL rises and falls differently in the number of holes, but this is replaced by the SUN DOWN signal obtained from the envelope generator 19 ゝ.

 Envelopment; 7 ° generator 1 9 inputs signals ARCLK and KEY

; '— Ο.νρί ■ • "Α'-, if-o Then, the direct addition of two-stage port cumulative addition: Insertion. Therefore, an 8-bit envelope signal (0,…, 7) is generated and the ^ -state of the trailing edge of the iron is generated. Generate a RUN DOWN signal indicating. The multiplier 20 multiplies the waveform signal "WG (0, ..., 1 1 :)" with the envelope signal EG (0, ..., 7) and sends the result to the DZA converter 21. The output of the / A converter 2 1 is sent to the vocalizer 2 2.

 According to the present invention, the repetitive waveform is such that one cycle includes a plurality of master clocks, and one cycle includes any number of master clocks. It is obtained by dividing into multiple steps including the clock and performing the multi-stage cumulative addition in synchronization with each step. Different waveforms can be obtained by changing the number of divided master steps or the number of master clocks allocated to each step, which can be changed with time. For example, it is possible to obtain a wave pattern that changes over time. In particular, it is known that, in the case of a musical sound waveform, the change in the waveform at the rising edge of the sound has an important meaning for the sense of fire. Based on this fact, in the case of Kanemiko's origin, we have provided a means to easily realize the change of the waveform at the rise of the sound.

Although the number of steps to be divided is arbitrary, a simple method is the division method as shown in Table 119. This is because the number m of ^ -octave low notes of each note is m = 2 X 2 in the case of 2-division, m = 4 X 2 in the case of 4-division, and the 2-division method is the 7th division. It is used to divide one station into 2 n steps as shown in the table, and the 4-minute l method is used to divide one station into 4 II steps as in the case of Table 5. One to use when splitting ¾ “Aru o _

 For example, the C tone (8 3 7 2 Hz) is a master included in one station-* number of clocks; ί '2 3 9 is 4 steps 5 9 6 ,

Evenly divide like 60, 60. The C tone of the 5th year old club is obtained by dividing the C tone of the 19th year table from the 2nd year old C tone of Table 19 by 2 steps. That is 16 steps. And the number of masters * included in each is 59,

60, 60, 60, 59, 60, 60, 60, 59,

6 0, 6 0, 6 0, 5 9, 6 0, w 6 0 and so on.

 Among the above waveforms, the number of steps in the eyebrows is not changed, and each step is shown. The number of masters * π ck contained in the change is o3, and the change is ^ 3 ". As in the example shown in Fig. 5 and Fig. 15, the number of clocks can be changed in each step, and the number of clocks can be changed.

 ^ One o as shown in

The number of cooks included in the step of the step is: Approximately ~ ~ ', and the remaining number 〇 The number of clocks in one step ¾ r g¾ A The total number of clocks included in the range is fixed to 1 Ό, and the number of clocks is adjusted if it is 3 Ό. The number of clocks is changed so that it is changed to ≤ £, and 1 ΰ .75? Is =? Ο is the natural amount of the relationship, and ¹ V is 3 ∑ of the sound. No ^: u.? \ There are some known changes, and in this case ¾, we also give ¾r ΖΞ.

0Λ-1ΡΙm. In the second case, that is, when the number of mouthpieces included in each step is changed almost uniformly, the number of mouthpieces is equal to each note name. The number of cooks is as shown in Table 20. In the table, the 1st column is the note name, the 2nd column is the note name code corresponding to ¾f, and the 3rd to 7th columns are the required data, respectively DT1, DT 2 and DT 3 , DT 4 and DT 5. DT 1 does not change the number of mouthpieces included in each step, and the quadrupling method shown in Table 19 shows the division of mouthpieces. It corresponds to the number. Table 20 shows that each of the four types of the four-division method in Table 19 shows the smaller amount of the cooked grains, but the modal mouth shown in Fig. 19 is shown. * This number is corrected as required by the X counter and, for example, in the case of the C sound, 5 9, 6, 0, 60, 60 are assigned to each step. Some come with clocks and some come with them. DT 2 to DT 5 are O data because they change the conical shape.

 D T 1 is against the number of stations of each sound, and, for example, it is one period of Fig. 17. In addition, D T 2 to D T 4 are the return-correspondence-type C shown in Fig. 17. It determines the rus ijj. Therefore, in order to obtain an a t ¾ c S shape that is not related to the note name, it is necessary to determine DT 2 ZDT 1 according to the note name to obtain a constant confidence. Become . D T 1 〜 ； D T 4 is not only remarkable if the pulse width is changed as shown in Fig. 17! : Is also used when changing :, and D T 5 is used when changing the local resistance from g to higher.

 C.v.PJ

,--. V.'irO ^

: ' The control ft No. 15 is mainly composed of the circuit shown in Fig. 20 and Fig. 21. Also, Fig. 22 shows a memory ^ that gives the initial and final deficit, and 2 3 ¾ shows an embroidery: ° force O circuit diagram. Although the figure shows the circuit diagram of the module X counter, 11 signal generators 15 are also configured including these.

As shown in Fig. 17 without changing the frequency of the configuration, the c If the Ru changing Le scan width is, the Ha ⁰ Norre scan Φ of the second FIG. 6) Ru Me determined E down Baie Lock off ^three c to te over as the first篛値given a DT 1 final as one likes And give DT 4. If the number of clicks included in this step temperature is changed from DT 1 to DT 4, it becomes c. The width of the Nores width, the user (Ha ⁰ Nores width and _¾ of the first period) is

Four four

 Change the station frequency from 1.0 to 0.4.

1 I 2 No change. Is it possible to change the Φ? ^ OPF (Ha ⁰ Nore A *) — ,, So 5-g -0 o

In addition, in order to give a change to the concussion number, it is shown in Fig. 23; Determine the number: For a 7 ° counter, give DT 5 as the initial value and DT 1 as the final value. About this _?-÷丄 1

 !-! '.' Yo 0.5 9 force to 1.0 ■ 'ί ^ i -3

 9 0

 F is a violence that changes the number of laps like this. Mode

(eguency m.de). Of course P «

It is also possible to use F-modulation and F-de-modulation ^, and this will be followed in actual cases. The memory group in Fig. 22 is ROM .: (Read Only Memo ry) is RA-Vl (Random Access

mo ry) · 3? Or it's o. Among them, the memories MEM1 and MEM4 store the data used for the P * mode modulation and F · mode modulation of the above. Memories MEM1 2 3 are the initial values of P · mode modulation, and memories MEM 2 * 2 4 are the final values of P · mode modulation.

 In MEM 3 * 25, the initial value of the so-called F-mode variation is appropriately returned from the table 20 and stored, and stored. The final'F 'mode is stored in the memory MEM 4 * 26, but this is only D T 1 in Table 20. The reason for this is that the intermodal change in the shape of the iron is remarkable at the beginning of the sound, and in the steady state, the local wave number is due to the varying frequency.

 These are: Memory ΜΞΜ1 SM4 is the note name code

• (T C 0, T C 1 T C 2 T C 3), and the data corresponding to each note name is S-forced. memory

 MEM1 .2 3, ΜΞΜ 2 24, E 3 * 2 5 is a 2-bit switch SW1 3 1 SW2 3 2, SW3 3 3 One of four types of data is returned ^ That's it. The data of the real alga given to the memories MEM1 to MEM4 is given as a negative number (an ϋ of 2) depending on the structure of one door.

 Next, we will explain the violence of modulo * X dew condensation, which is a contract to change the number of kukukku contained in each step for each step. Prior to this, it is necessary to consider a little about the concavity O S ij.

Observing the ¾ Φ of the natural musical instrument sound,

o

 As a result of the annoyance, the pitch becomes higher, and the amplitude becomes a little smaller, but it is not so constant and there is no L. In the case of Electronic Music II, ◯ is also similar to this. In the case of waveform synthesis by multi-stage ^ cumulative calculation, the width is 1 and C 2

 It was shown to depend heavily on the number of tapes. For example, 2 steps

 Included in one cycle when approximating the sine function by the cumulative cumulative calculation.

 If the number of steps is 4 η, then Cxi is C and C is

It was (E0) _k salary). If we interpret this as having 0 as a medium and having a number of dragons in the positive and negative directions as well, we consider the maximum swing η to be a large swing Φ value and assume that it is a person 1. The goal is the meeting.

Ύ 乂 1 9 Minutes from the 4-minute method 7 shown in the table ;! Then, in case of getting 1 ¾ ¾ of the sound ≥ i according to the octave 51 :! = 2 ⁷ - 'and that Do not. Here, ^ is an octave number, and in the table of l9, © is the 7th-year group, 7 is ¾έ, and c = ₂ ² ~ ^.

-0. No arithmetic operation is required to obtain this value, and only a shift operation can be performed, so it is practically possible to use hardware

 hardware) does not increase. It is displayed in binary, and can be adjusted to a real number depending on how to solve the D-position of several points, and can also be a large number / i, and a large number. That is, there is a case where the second haze is used as a unit ^ ^ ¾ ¾ fi. When adding, especially when calculating the a position of the grain point,

CMP3 i ^: ' ^{i: 0} There is no contradiction. Based on the above discussion, it is possible to understand in real terms the aid of the concise shape. In Table 21, we give 5 kinds (15) of modulation index I for each note name, when the maximum contact of the varieties of grains under the MO- 'X subcontractor is classified as S1. Ώ.

 21st table, F

Note name _Λ i!

TCG TC1 TC2 TC5 I 1. \ I 2! I 3 I 4 ί I 5 1

 ί ίί!

! :

 0 0 0 0 63! i 35 is!

 ! ! ! ί

 0 0 0 60! Shi '? 17: 0;

 \ •

 1 D "0 0 1 0 56 \ 48 ； 16 ； 0 j

 !

E 0 0 1 53 45 i 30 15 ； 0！

 I

0 1 0 0 \ 2 ί 28 14 _: 0! n ϋ; 0 '7:

: G 0 1 u 44 ； 38 ： 25 丄 ο ^; 0!

! i

1: ；

 G "0 A

 1-. Ό 12: υ

 I!

 A 1 0 0 0 40 ο ο

 11! 0!

 (

! "!

 0 0 1 33 11: o j

 "ί i

*-―

 H i

 1 0 i o '30 1 10 'n: ί

 ι 1

 1 1 0: 33 19 9 .o;

,

 Ma, '

, D ', ； If the subcontracting index is different for each name, it is because the phonetic name is given a gallling-one-obvious ¾ ^ G S ¾ as described above. In addition, the ratio II / DT 1 of 箅 et al 1 and DT 1 in Table 20 is-

 Since they are almost constant, they are mutually dependent. In 2 2 ¾, memory ΜΕΜ 5 2 7 is the WM value of the metamorphic exponent. In memory MEM 6 * 28, the final value of the metamorphic finger ¾ is stored as 4 types of Ο data by note name. It is. One of these four types of data is the switch SW 4 "34 and SW 5-, respectively.

3 5 and the data for each note name is changed to the note name code.

It is redeemed by T C 0 to T C 3. The amount of data stored is negative (20).

 ¾ 9.

In memory * 2 9 the second ≤ table. © 'Data RDT 1 force; can be stored. The data DT 1 from the O data table 20

I

 Set the distance between F 4 and G O to ¾ :! ¾ is ¾. Two powers

 This is because we give g ^ a change in time ¾ with this ¾ 0 real ¾ ^.

 It is a counter-comparative example of a local clock of 0 clocks, which is used as a counter. This means that the time required for the change in ^ is set to a certain level that does not exist in the note name.

 For example, the modu π * X variant is so-called table grain.

1 I: 3 ο COUNT (difference in variation index, or 6 3 — 1 8 = 4 5 for C tone, for example) is from DT 1 in Table 20. If the counter moves the counter 0; ^ ¾ is changed to DT 1 ϋ Ι¾ (thus, it is against RD? 1 in Table 2 2). The required information is constant regardless of the ministry name. Memo U JIEM7-29 is based on the note name Koichi (? C0-: C3). In this case C as well, the data stored is food. In the memory MS MS * 30 0, the data-one BDT in the table 2 2 is stored in each note. This data is a 2-bit data, and is stored in the module Χ counter shown in No. 19 and cooked in 1 step. ============ 2 C phonetic note: The corresponding DT data 5 9 is added, and the number of clocks included in each step is 5 9, δ 0, 60, 60. In order to remove these four steps, '' ^ ^ Ο is ο ο ο emo ') Μ Ξ Ivl ο-3 ΰ' / 专⁼ 1 word TC 0

T C ': 5¾

 N ^ as ί ',

'-

' The envelope counter is shown in Fig. 23 and is used in the control signal generator shown in Fig. 20. Reply These envelope counters have various types of c to change the musical tone waveform with time. The parameter (for example, the number of clocks contained in one step, the modulation index of the zero, and the modulation index of the zero-X modulation) is given as a function of time. 7 ° · The components of the counter are as shown in Fig. 23, an 8-bit upper Z-down, a counter 1 36, 8-bit. Tsu door of co-down c ^0, single-data one 3 7, NAND Ke ,, - door 3 8, 3 Ru 9 and Lee emissions path over data one 4 0 der. The input terminal is a CK terminal 4 2 which drives the power counter 1 3 6 and a terminal 4 1 to which a data input XI (0, ..., 7) to the counter is given and a connector. emissions c ⁰ B input data X 2 to record COMPUTER 3 7 (0, 7) Ru terminal 4 4 der you烘給a. Output terminal is a connector. It is also the terminal 45 that is supplied to the A input of the laser 37 and is given the output X 0 (0, ..., 7) of the counter 36.

Time change Ti Ha ⁰ ra one Turn-initial value X 1 (0, ..., 7 ) of the given applied to the input terminal 4 1, the final value X 2 ((),. · ■, 7) the input terminal Give to 4 4. The initial value X 1 (0,…, 7) is the I CLR signal and is loaded into the power counter 36. Meanwhile co down Ha ⁰ Les COMPUTER 3 7 its inputs A, B of the <"1" to Yui鎳4 6 if B of al, A> A compares the values B of al Invite to Yui鎳4 '7 "1" is output. These hooks 4 6 and 4 7 are connected to the NA D gates 3 8 and 3 9 respectively, and the counters 3 6 It serves to gate the clock CK from the terminal 42 which will rot. That is, the clock CK is applied to the UP terminal 4 8 of the counter 1 3 6 that is A or B, and the CK terminal is applied to the DOWN terminal 4 9 of A> B. become . In addition, when the input is A = B, the counter ⁰ -three-third-thirty-seven-three-three-four-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-three-th, and the-thousand-thousand-thousand-third-th data recording shows the 0-th data. Stop the unit. That is, this envelope. In the counter, from the initial value X 1 (0,…, 7) given to terminal 41, the speed is proportional to the frequency of the clock given to terminal 42. It shifts to the final value X 2 (0, ..., 7 :) given to terminal 4 4 and appears as output X 0 (0, ..., 7) at terminal 4 5.

The Modulo X counter used in the control signal generator used for the development shown in Fig. 20 has the circuit configuration shown in Fig. 19 .. In this embodiment, one cumulative addition is made in one step, but the Modulo X counter produces a synchronization signal for that purpose. The input of the module X counter used for this purpose is 8 bits of data X (0,…, 7), which is 8 bits depending on the terminal 50. It is applied to the data input of the first counter 51. MCLK is the master clock that drives the counter 51, the counter 5 3 and the flip * flop 5 4. The LD terminals 5 5 are respectively connected to the NOR gates 5 6 and the counter terminals 5 7 through the counter terminals 5 1; the LD terminals 5 8 and the counter terminals 5 3 are connected through the LD terminals 5 5 and the counter gates 5 7 respectively. Connect it to the CLR terminal 5 9 and the reset terminal 6 0 of the flip-flop 5 4. The other input is This is a 2-bit BD (0, 1), and is the select signal of 4-way selector 62. Input data X (0, -...-,

7) is externally applied to the L D terminal 5 5 and is loaded to the counter 5 1 and the clock MCLK and K :. The counter 5 1 counts the clock M C LK, and outputs the ripple key 6 3 by connecting it to the personal computer. For example, if the input data-X (0, ···, 7 :) is given 1 59, the ripple * key is output at the 5 9th count. This ripple carrier is fed to the A input of the 2-way selector 6 4 and is delayed by 1 clock by the flip-flop 5 4. It is then fed to the B input of the selector 1 64. The selector 1 6 4 selects one of its inputs A and B and selects its output 6 5 as the load signal and counter of the counter 5 1.

5 3 signal signals 6 6.

Therefore, if the A input is selected and output by the selector 1 64, the new data X (0,…, 7) is counted 5 9 and then the counter 5 1 If the B input is selected, new data will be loaded after 60 counts. The output 6 5 of the selector 6 4 has 5 9 counts after the data is first π-, and is 60 clocks 1 clock wide. Output the ^zero loss of. Selector

Which of the inputs A and B of 6 4 is selected depends on the output Y of the selector 6 2 supplied by the concentrator 6 7 and the logical value of the output Y is ο. Select A for "0" and Β for "1". The counter 5 3 is a 2-bit 6 4 output c. The same output is repeated each time four pulses 65 are generated. Therefore, "0 0 0 0", "0 0 0 1", "0 1 0 1",

Ha of "0 1 1 1". Turns occur repeatedly. This four Ha ⁰ data one down of cormorants Chi Le, The choice of the deviation of the Selector Selector Address one 6 2 Selector Selector door signal S 0, is input to the S 1 data BDC (0, 1) It is decided by. This BDC (0, 1) signal is supplied from the memory MEM8 shown in Fig. 22 and has a different message for each note name.

 OUT 1 is the output signal of the selector 6 4.QUT 2 uses OUT 1 as the counter 5 3, the inverter 6 8 and the NOR gate 6 9 as 1 It is a step division. For example, if the input X (0, ..., 7) is connected so that the output of the memory MEM 4 in Fig. 22 is supplied, and if the C tone is pressed, the tone is played. The name code TC (0, "', 3) becomes" 1 0 1 1 "and the input X (0,…, 7) is given 1 59, and BD (0, 1 ) Since "1 1" is given to the signal, the D input of the selector 1 6 2 is selected, and the outputs OUT 1 and OUT 2 are shown in Fig. 24 (a). As shown, it occurs in the 59th and 60th counts, and in the 1 1 9th and 120th counts.

The control signal generator shown in Fig. 20 is the same as the engine * counter shown in Fig. 23 and the modular X counter shown in Fig. 19. Various signals are generated by using the two elements of and as components. The IC LR signal in this figure is the initial clear or data load signal o of the registers and counters before waveform generation. As a result, it is obtained. —

 The module Χ counter 70 is used as the X input and the data R (0,…, 7), which is directly proportional to the note name frequency from the memory ΜΕΜ7 in Fig. 22. Is given to output OUT 2, a clock with a frequency that is inversely proportional to the pitch frequency. Loose rows are born. This ha. The sequence of pulses is divided by the binary counter 71, which is initially cleared by the output of the damper 78. The 8-bit output of the counter 71 is input to the five-way 8-way selectors 7 2, 7 4, 7 6, 2, 0 0 and 2 0 2, respectively. One of the eight bit ffi forces is selected ffi force at each of chi 7 3, 7 5, 7 7, 20 1, and 20 3. The outputs RCLK1, RCLK2, RCLK3, RCLK4, and RCLK5 of these selectors are different for each note name so that the time required for waveform change does not depend on the note name. It is a clock with a frequency.

 The modular X counter 7 9 is given as the X input by the data N (0, ..., 7) from the memory ΜΕΜ 4 2 6 in Fig. 22. C that is proportional to the note name frequency. Envelopes that form the loss train ETCK: τ ° · Counter 8 0 changes from initial value FI (0, ····, 7) to final value N (0,…, 7) Till clock

It counts RCLK1 and sends the intermediate value FT (0, ..., 7) to the module χ counter 8 1. The frequency counter 1 8 1 has a frequency that changes with time based on this data. Generate the loss sequence FT CK. This Ha ⁰ ls e column FT CK et al used to Ru given the time changes in the frequency of the tone ',', '"" 0-- This.

E down Baie Russia-up mosquito c te over 8 2 temporal Ha ⁰ le scan width of the approximate co-Size Lee down Ha ° le scan waveform, such as the first FIG. 7 Chi match for be modulated P · mode To change to. Count the clock RCL 2 from the initial value PI (0,…, 7) to the final value PF (0,…, 7), and set the intermediate value PT (0, ····, 7). ) Is output and is used as the B input of the adder 8 3. Another input A of the adder / adder 8 3 is the upper 8 bit port G (0,…, 7) in the output MWG (0, ..., 19) of the modulated wave generator 16 Is. The lower 12 bits G (8,…, 1 9.) are ORed at 0 R gate 8 4 and ANDed with the highest bit (sign bit) MWG 0. , 8 inputs. The output of the AND gate, 8 5 is applied to the carrier input CI of the adder 8 3.

 The control of such carrier input is performed by subordinate to the positive and negative data VG (0, ····, 19), which are represented by the two's complement representation with equal absolute values. 1 This is because when the 2 bits are discarded, the absolute values of the upper 8 bits that have been discarded are made equal. This operation is necessary because it is necessary to satisfy the expression ^ for modal modulation. The output of the adder 8 3 is the number of master clocks included in one step when Ρ mode modulation and module X modulation are performed simultaneously. ΡΧΤ (0,…,

7) comes out. This ffi force is a modular

This is the X input of 8 6. The signal FCRY, which is the input of NOR gate 8 8, is the ffi force of the modular counter 8 1.

When counted individually, it is a signal that becomes "1" for one cycle of the master clock MCLK.

The PCRY that is the input of the NAND gate 8 7 has only one cycle of the clock MCLK when it counts 2 ⁿ PTCK that is the output of the modular X counter 86. It is a signal that becomes "1". Where n is a positive integer that depends on the type. For example, in the 5th year group, _n = 4 and 2 ⁿ = 16 is the number of steps of waveform synthesis by cumulative addition. Ha. Two Ha of Ruth PTCK. The number of masterpieces included between the louses is c. Ls e FTCK of two teeth ⁰ Le rce small also Ri by Ma scan Turn-click-locking the number contains or is Ru in Les, of the, you prior to the c o ls e PCRY Ganoya Angeles FCRY o PTCK If you count 2 ⁿ , you will get c. The output Q of the flip-flops 8 9 is set to a logical value "0" by the loss PCRY, and the output Q is modulo X 0 by the AND gate 90. Inhibit the output OUT 1 of the printer 8 6. Therefore, after this, ha. Loss PTCK does not occur. After that, ha. Ls e FCRY by Ri off Clip off the furnace-up 8 9 is cell Tsu door, the output Q of the Soviet Union that occur again Ha ⁰ ls e PTCK and ing to the logical value "1".

 Ha at the same time. Loose FCRY loads the data PXT (0,…, 7) to the Modulo X counter 86. Figure 24- (b) gives the timing diagram of these signals when n = 4. Envelope counter 1 9 1 is initial value X I

(0,…, 7) to the final value XF (0,…, 7) are counted, and the clock RCLK 3 is counted, and the intermediate value thereof is the modulation index I of the modular modulation I ( Output as 0,…, 7),

OMPI _ Flip '7 loft in Figure 21? .92 is used to synchronize the KEY signal with the clock MCLK. This output Q is input to the flip-flop 93 and the NAND gate 94. A flip-flop 9 3 and a NAND gate 9 4 form a differentiating circuit, and the NAND gate 9 4 is connected at the head of the KEY signal.

 Generates I CLR signal. NAND gate 9 9

ICLR is input and PSTP signal is generated.

 The flip-flop 10 2 is set by the ripple 1 0 5'counter 1 0 5 ', and is set by the signal ICLR.

It is reset by the output PCYC of the NOH gate 1 0 1 that inputs PCRY. LDCYC = "0", LDCYC = "Γ, when the flip * flop 10 2 is reset, and therefore the counter 100 0 is (ABCDE)-" 0 0 0 1 1 "is input. Fri: ° · When the floppy 1 0 2 is set, LDCYC =" 1 ", LDCYC =" 0 "starts counting. (ABCDE) = "1 1 0 1 0" is input to 1 0 0

 In the case of the former, the counter 100 outputs the ripple carrier 10 at the time of 7 count, and in the case of the latter, it outputs at the time of 20 count. I will be here. Nao counter

Input data to 100 is a clock MCLK, signal

It is done by PSTP. The signal PCYC is a signal synchronized with one cycle of the waveform, and the signal PSTP is a signal synchronized with each step in one cycle. At the first step in the cycle, at 7 counts, ripple carry «ΟΛΙΡΙ WiPo-, Output, and the other steps output a ripple carrier when the count is 20 '. Frits: τ ° · Floats: 7 ° 10 3 and NAND gate 10 4 are synchronized with one period of the waveform, 7 in the first step and the rest in the remaining steps. A clock signal WMCLK containing 20 clock MCLKs is generated <Figure 24-(C) is a timing diagram of these signals and they are included in one cycle. This is the case when the number of steps is 4.

 The octave code 0 C (0, 1, 2) from the keyboard controller 14 is coded by the decoder 1 9 5 and its output is read from each column. Outputs through the counters 196, OCTl, OCT2, OCT3, OCT4, and OCT5, the counters 1 2 8 and 1 2 9 in which only one of them is "1" are musical tones. The number of PTCs included in one cycle of the waveform determined by the group of people to which it belongs. And then sends the ripple carrier PCRY as output 1 3 2 from the counter 1 2 9. The OR gate 1 2 7 supplies the data that loads into the counter 1 2 8 to its input (ABCD), so the signals OCT 2 to OCT 5 are input. It is being touched. OCT 1

When 1 ,, when (ABCD) = "0 0 0 0", OCT 2 = "1, When, (ABCD) =" 0 0 0 1 ", When OCT3 =" 1 "(ABCD) = When "0 0 1 1" and 0CT4 = "1" (ABCD) = "0 1 1 1", when OCT 5 = ^rt l "(ABCD) =" 1 1 1 1 ".

This data is loaded to the counter 128 in synchronization with the I CLR signal and starts counting the clock MCLK. The counter 1 2 8 is an over mouth, which causes the ripple carrier to output a new signal to this counter 1 2 However, at the same time, it also advances the next counter 1129 by one count. The counter 1 2 9 is a 4-bit counter, and therefore the counter 1 2 8 of the ripple and the carrier is 16 counts. Output the ripple carrier 1 3 2 PCRY. Say

When OCT2 = "l" (A B C D) = "0 0 0 1", every 8 counts — 1 2 8 overflies. Therefore, the ripple carrier 1 3 2 comes out from the counter 1 2 9 when 8 X 1 6 = 1 2 8 counts are completed.

 The contents of the counter 1129 are delayed by one step time (one cycle of the pulse PTCK) in the latch circuit 1331. The output of the latch circuit 1 3 1 outputs the signal IHB and is also supplied to the exhaust single-chip OR gate 1 3 0 and the signal as shown in Fig. 33-d is shown. Output PXOR1 and PXOR2. These signals are delayed by one step time by the latch circuit 1 3 1 because the first step of the waveform calculation is applied to the initial value load. First, the cumulative addition will be performed from the next step.

 The connections of the counters 1 3 4 and 1 3 5 are the same as those of the counters 1 2 8 and 1 2 9 and, therefore, operate similarly. In this case, the counters 1 3 4 and 1 3 5 are equal to the number of steps included in one cycle of the waveform determined by the group of musical tones. Outputs a ripple key FCRY each time it counts the FTCK of the talk FTCK.

, O PI FCRY and ICLR are input to the gate 1 3 7 and the FCYC signal is generated.

 Modulated wave generator 16 has the circuit configuration shown in Fig. 25. The latch circuit 10 6 latches the data I (0, ... 5) that determines the amplitude of each period of the waveform with the clock PCYC. Shift register for each step107.

Then, in synchronization with the clock MCLK, the lower bits are output in sequence from the lower bit to the connection port 1108.

 Imperator 1 109, Selector 1 110, NOR GE, 1

 The 1 1 2 and the flip * floppy 1 1 3 form a two's complementer. Whether or not the two's complement is taken is the NOR gate.

It is controlled by 1 1 1. That is, the NOR gate 1 1 1 is configured so that its input is complemented when .LDCYC = «1" or PXOR1 = "1". LDCYC. It is a signal that is synchronized with the first step of the waveform, and this step loads the initial value to register 120, but this initial value Is taken by taking the two's complement, which is because the signs of (R ² ) a and (R0) _Q in Table 3 are opposite.

Assuming that one cycle of the waveform is 4 n steps, the signal PXOR1 has ⁿ 0 "at the first ⁿ steps and" 1 "at the next 2 n steps. It is a signal such as "0," on the tape. That is, the 2's complement is taken at the middle 2 n steps. The reason for this can be _clarified by referring to (RO) _{k in} Table 3.

 The shift register 1 1 2 1 and the AND 'OR gate 1 2 2 output the output of the selector 1 1 0 to the signal OCT (1, ..., 5).

f OMPI, The number of corresponding bits is shifted and sent to the cumulative adder. The number of steps included in one cycle differs depending on the age group, and thus the difference in amplitude occurs, but shift registers 1 1 2 1 and AND, The OR gate 1 2 2 has a function of removing this difference and standardizing the amplitude. The difference of one octave is twice the number of steps, and therefore four times the amplitude.

 Selector 1 2 3 selects either output 1 1 4 of selector 110 or AD * 0 H, and output 1 2 2 of output 1 2 6 depending on signal LDCYC. Suru. The LDCYC signal has a logical value of "0" at the first step of one cycle of the waveform and a logical value of "1" at the remaining steps. This signal selects inputs 1 1 4 on the first step and inputs 1 2 6 on the remaining steps to send to the accumulator adder: ° The first cumulative adder is composed of the flop 1 15 and the adder 1 1 6 and the register 1 1 7. The flip-flop 1 15 sends the carrier generated as a result of addition to the upper bit. The flip 7 loop 1 1 5 is reset with the signal PSTP at the beginning of the calculation of each step. The shift register 1 1 7 has a length of 20 bits and is cleared by the LDCYC signal at the first step of one cycle. This accumulator is driven by a clock WMCLK that contains 20 clock MCLKs in each step, except the first step in one cycle of the waveform. It is The output of register 1 1 7 is fed back to adder 1 1 6, and at the same time, adder 1 1 9, flip-flop 1 1 8 and register 1 1 2 Consists of 0

Ο 'ΡΙ Is input to the second cumulative adder of _σ, which is the initial load at the first step of one period of the waveform, and the remaining load at the remaining step. The output of the first cumulative adder is further cumulatively added. The output of the shift register 1 120 obtained in this way is latched by the latch circuit 1 3 6 and the signal MWG (0, ..., 1 9) to the control signal generator 15

 The concrete circuit configuration of the modulated wave generator 17 is as shown in Fig. 26. The circuit configuration of the modulated wave generator circuit elements 205 to 210 is shown in Fig. 25, which is the circuit element of the harmonic wave generator 1 0 7 to 1 1 3. The circuit operation is the same as that of the circuit configuration, and accordingly, the same operation is performed. When the amplitude of the waveform is not changed, the switch SW W 1 1 · 2 0 4 is used to give a fixed amplitude value. At this time, if the Β input of the adder 220 is a logical value "0", the waveform as shown in Fig. 27- (a) is obtained (here, there is no modulation for simplicity. Consider the case).

 Also, the circuit configurations of the circuit elements 211 to 217 are almost the same as the circuit configurations of the circuit elements 204 to 210. The difference is that one input of the NOR gate 2 17 is the signal PXOR2 and that the selector 2 1 4 is equipped with the strobe terminal STRB. .. When IHB = "1", the logical value of the output Y of the selector 2 1 4 is always "0". The signal PXOR2 is a signal as shown in Fig. 27-d.

 2 bit shift register 2 1 8 and selector

o pi .wn o 2 1 9 is for adjusting the amplitude. In other words, the waveform obtained by using the signal PXOR2 at the input of NOR gate 2 17 is one as shown in Fig. 27-b or Fig. 27- (c). This is the haha. Since the number of steps assigned to each pulse is half that in the case where the signal PXOR1 is used, there is an imbalance in which the amplitude is 1Z4. It is the shift register 2 18 that adjusts this. Unless the input IHB of the selector 1 2 1 4 is always set to "0" and the output Y is not prohibited, the waveform shown in Fig. 27 (-bj is obtained. -By using the signal of (d) and prohibiting the latter half of one cycle, the waveform shown in Fig. 27- (c) is obtained, and the input of PXOR2 of NOR gate 2 1 7 is obtained in this way. Or, if various signals are applied to the input IHB of the selector 1 2 14, various waveforms corresponding to the signals will be obtained. The outputs of 2 0 7 and 2 1 9 are added and sent to the shift register 2 2 2.

 Shift register 2 2 2, AND 0 R ,, 1 2 2 3, Selector 1 2 4 4, Fri: τ ° · 2 2 5, Adder 2 2 6, shift register 2 2 7, flip * flop 2 2 8, adder 2 2 9 and shift register 2 3 0 The connection method and control signal are the same as the corresponding ones of the modulated wave generator shown in Fig. 25, and therefore the same operation. In the register 230, the waveform shown in Fig. 27- (a) and the waveform shown in Fig. 27- (c) can be added to obtain the result. .. In addition, the ratio of the individual waveforms included in this composite waveform is expressed by the switches SW 1 1 2 0 4 and SW 12

O'.PI , 2 11 1. The register, the numerical data 1 calculated in τ 230, is in 2's complement notation and is inconvenient for multiplication. Then, it is converted to a single-manifold display by a single 0H 2 3 2 and is latched to the latch circuit 2 3 2. , The modulated waveform signal WG (0,…, 11) is sent to the multiplier 20. Usually, the musical tone waveform is divided into three parts. That is, they are rising, steady, and falling. These three parts are obtained by controlling the amplitude of the waveform. This control usually involves multiplying the waveform as shown in Fig. 28 (a), which is called the opening: 7 °, with the periodic waveform in Fig. 28 (b). Suru. You can obtain the tone waveform shown in Fig. 28 (C). The part indicated by T _A in Fig. 28 (a) corresponds to the rising part, the part indicated by T _D corresponds to the falling part, and is sandwiched between them. part is Yo I Do E down downy mouth-up of to that o the second FIG. 8 corresponds to the steady part (a) of Cross - 3 ¹ Ri by the cumulative addition method "Ru Shi door can be. for example, the first 3 _{Consider the} function (R ² ) _k by two-stage cumulative addition as shown in the table and Fig. 9. The time _k is synchronized with the rise of step k = 1 to 8 of this function. Calculate at intervals of _k = 'and accumulate at the end of k = 8

 o

Stop adding. Therefore, after that, the waveform keeps the value of (R2) ₈ = 16. Next, at the falling edge, cumulative addition

 T

Restart the step: ° k = 9 to 16 at time intervals.

 8 If the calculation is done, the inlet waveform in Fig. 29 (a) can be obtained. Again

 T

Step: Calculate k = 1 to 12 at time intervals with _A = and

0 Λ Ι W; FO After suspending and resuming, if step k == 1'3 to 16 is calculated with _D = ~ ^ at time intervals, the envelope waveform in Fig. 29 (b) can be obtained. Figure 29 (a) is suitable for synthesizing the waveform of woodwind instruments, and Figure 29 (b) is suitable for synthesizing the waveform of brass instruments. It is clear that the above-mentioned π-shaped waveform also comes out by calculation by cumulative addition.

Next, in order to obtain a waveform whose amplitude changes with time, for example, a waveform like that shown in Figure 28 (C), the waveform is obtained as shown in Figure 28. It is shown that it can be realized without multiplying the loop waveform and the periodic waveform. The functions shown in Table 23 are (Rl) ₀ = (R2) 0 = 0, and (HO), is 1, 4, 1 3, 3, 5, in 4 step units as shown in the table. It is assumed that the values of,-5,, -7, 7, 8,, -8, -8, 8, ... From step 3 2 onwards, a function with a period of 16 steps similar to that in Table 3 is used. The function value (R2) _k of the step k obtained by this is calculated for each step? When cumulative addition is performed for each unit time, a waveform with a change in amplitude with time is obtained as shown in Fig. 30. This hits the rising edge of Fig. 28 (c). Similarly, it is known that the waveform corresponding to the trailing edge can be easily obtained. The waveform in Fig. 30 has positive and negative amplitudes, but if only positive values are needed, the function in Fig. 4 or Fig. 31. It is possible to easily create it from the function of.

ΟΛ'ΡΙ

, Ν, ', Γθ

H 32

 12

/62.df/XOJ 99120/08 OA This envelope waveform is created by using the output signal ARCLK of the'a 'and the disk deck o'clock generator 18 and the KEY signal from the keyboard control unit 14. O performed by the loop generator 19

 Figure 32 is a detailed circuit diagram of the attack and delay clock generator 1 8. This circuit is a master clock.

The purpose is to divide the MCL to give a clock to control the speed of the rising edge of the waveform and the falling edge of the waveform. The rising and falling times of the waveform are different depending on the musical tone.) Therefore, in this circuit, a predetermined one can be selected from various clock frequencies. Also, the rising and falling speeds can be set independently. In normal music, the rise time]) is usually smaller than the fall D time.

 The counter 1339 gives rise to the ratio of the clock frequencies of rising and falling]). The RUN DOWN signal is a signal that becomes "1" when the waveform falls]) and is generated by the envelope generator 19. EU DOWN = "1" when in the rising]) state: ^ et al counter 1 3 9 has (ABCDEF) =

 "001111" Force S is input. This data is loaded to the counter 1339 each time a ripple carrier occurs. Therefore, the ripple 'carrier of the counter 139 is generated every 4 times the clock MCL is powered.

 In the falling state, RUN DOWN = "0", so (ABCDEF) = "0 0 00 0 0" and the ripple carrier

 Hi ^ ^

CV.PI Occurs every time the clock MCLK is counted 64 times. This ripple carrier will be further hung by the next counter 140. The number of counts is determined by the input data 1 [ABCDEFGH) to the counter 1 140], which is the switch SW7 · 1 43 when RUNDOWN = 1 ". , RUN DOWN = "0", switch SW6 · 1 42 to selector 141]? Is selected.

 Data on the rising edge set to switch 1 4 3 or data on the falling edge set to switch 1 4 2]? 1 to counter 1 4 Ripple of 0'frequency power of carrier ARCLK; determined. If the frequency of the master'clock MCLK is 2 MHz, the cycle of the clock ARCLK is 4 for rising; "~ 5 12 sec, falling]). Will be 6 4 "~ 8 192 i see. Clock ABCLK is sent to the engine; ° generator 19.

 The detailed circuit diagram of the envelope generator 19 has the configuration shown in Figs. 33 to 35. Circuit 1 144 in Fig. 33 generates the signal CLEAE to initialize the system when the power is turned on. Flip; 7 ° · Flop 145 is the key generator that is generated when the key is pressed.

The output is called the signal KEYON because it synchronizes 19 with the active clock ARCLK.

Flip: ° · Flop 1 46 and NAKD Gate 1 47 constitute a differentiating circuit whose output RSET is a flip-flop, a counter, a register. Reset of the target, Kur 1] Ear, load Used as. Flip-off: 7 ° 1 4 8 is reset via CLEAR signal when system power is turned on]? NOR gate 1 4 9 Set by the EYO signal. The flip-flop 1 48 is reset again according to the ATEND signal that is output synchronously at the end of the calculation of the rising edge of the waveform] ?. Flip 'Float; τ ° 1 48 8 ATTCK = "1" when force is set, which is "Waveform i? Calculation is possible or is being performed. "Corresponding to this.

 Flip Flop 1 5 1 depends on CLEAR signal]) NOR Gate 1 5 2 resets to KEYON signal generated when the keyboard is "OFF"]? It will be done. This flip-flop is reset again by the RDEND signal that is output synchronously at the end of the calculation of the falling edge of the waveform. AND — The output signal RUN DOW of 1 5 3 is set to 1 'if flip' block 1 5 1 is set and at the same time ATTCK = "0" or rising 3 is calculated. To Therefore, the RUN DOWN signal corresponds to the fact that the falling edge of the waveform] can be calculated or is being executed.

 The output signal ACTIV of the OR gate 150 is equal to the logical sum of the signals ATTCK and RUN DOW. Because ACTIV = ATTCK +

DECAY = ATTCK + ATTCK · From DECAY = ATTCK + RUN DOWN ft. That is, the ACT IV signal rises in the waveform! ) Or corresponding to the fact that the falling edge is computable or is in progress.

 The control signal generator of the amplifier π

CV.PI Vi O Have the circuit configurations shown in Figure 34 and Figure 5 respectively. In this case, the calculation of the total π-top is based on the two-stage cumulative addition as shown in Fig. 29, and at the same time, the straight-line interpolation as shown in Fig. 7 is performed. Assumed to be performed .

Immediately, another 16-step straight-runner is carried out between each step of the two-stage cumulative addition with 16-step shown in Fig. 29. Therefore, the total number of steps is 1 6 X 1 6 = 2 5 6.

 0

 For synthesizing woodwind sounds (full-tone, clear-net, etc.), 1 out of 2 5 6 steps is set to 1 2 8 steps, and 1 2 8 Steps are assigned to falling (see Figure 29 (a)). For brass sounds, it uses 1 9 2 steps to start up and the remaining 6 4 steps to start up.

 Table 24 shows how the value of the first and second changes with each step. In this table, the resisters R l, R 2'- are the eight-bit ones 1 6 9, 1 in Fig. 35, respectively.

Corresponds to 1 7 4. The value of (H l) _k in steps 2 40 to 2 5 5 is zero, but it is effective up to the actual 2 39 steps, but the hardware is Due to the air structure, it is more convenient to handle all parts up to 2 5 5 steps. The value of (R 1) _k is k = 16 n

(n = 0, 1, 2, 2, ...) increases by ± 1, and the noteworthy value is the number of steps k = 16 n and k = 16 n — 1 (n = 1, 2 , 3,…) and the values of register R 2 are the same, that is, (R 2) _{1 6n} = (R 2) _10n _ ₁ . This is (R2) _16n

Don't add up ^!

OMPI However, the reason for prohibiting cumulative addition once in 16 times is as follows. That is, unless we ban

The maximum value of (R 2) _k is +2 5 6, which means that the expression ffi does not come in 8 bits. This is because the positive value that can be expressed with 8 bits is from 0 to +2 5 5.

 By prohibiting the cumulative addition once in 16 times, it is possible to limit the maximum value to 2 5 6X ^ "= 2 4 0 in this way.

CMPl Table 24 Table k 0 1 2 ·-15 16 17 18 · '• 31 32 33 34 ·-· 47 48 49 50… 63 64 65 66 ·' · 79

(Rl) _k 1 1 1 · '• 1 2 2 2 ··· 2 3 3 3 * • 3 4 4… 4 3 3 3 ·-3

(R2) _k 0 1 2-• 15 15 17 19 ··· 30 30 33 36 · · 90 90 94 98… 150 150 153 156--195

106 107 108… 111 112 113 114… 127 128 129 130… 143 224 225 226… 239 240 241 242… 255

1 1 1 ... 1 0 0 0-0-1-1-1 ...-1-1-1-1 ...-1 0 0 0 ... 0

225 226 227… 240 240 240 240… 240 240 239 238-225 15 14 13… 0 0 0 0… 0 ― "'--■,'

Each step for synthesizing the full-top waveform by the two-stage'third-order cumulative addition in Fig. 3 4 and Fig. 35 is 8 bit time, that is, This is a hardware configuration that is calculated by using eight clocks ARCLK for dynamics. The first of the 8 bit times required for the operation of each step is called the 1st bittime, and the 8th one is the 8th bit. 'This is called a time. The counters 1 54, 1 5 6 and 1 5 8 in Fig. 34 can be counted only when ACTIV = "1".

The output CRY 1 of the NOR gate 1 5 5 is "1" at the first bit'time of each step. The output CRY 2 of NOR gate 1 5 7 is a signal that starts from the 0th step and becomes every 8 bit times "1" every 16th step. The outputs of the exclusive OR gate 1 59 are all 0 bits at steps 0 to 63 and all 0 bits at the step 0 to 63. 8 bit time "1", steps 1 92 2 to 2 5 5 make all 8 bit time "0". Therefore, the output of the OR gate 1 63 is steps 0 to 63, only the first bit time is "1", and the steps 64 to 191 are all output. 8 bit time “1”, status: 7 ° 1 9 2 to 2 5 5 and the AND gate 1 6 4 of only 1st bit time becomes “1”. The output PMONE is steps 0, 1 6, 3, 2 and 4 8 and only the first bit time is "1", and steps 6 4, 8 0, 9 6 and 1 1 2,. 1 8 8, 1 4 4, 1 6 0 and 1 7 6 all 8 bit 'time becomes "1", and the steps 1 9 2, 2 0 8, 2 1 4 and 2 40 Only the time signal is a signal that becomes ".1".

The ripple-carrying output RDEND of the counter 1 158 is in the step ° 2 5 6 from ^w 0 "to ^w 1". It is used as a signal indicating the end. Selector

 ATEND, which is the output of 1 61, is a signal that changes from "0" to "1" at step 1 2 8 or from ".0" to w 1 at step 1 92. One of these signals is selected and output by switch 1 62. ATEND is used as a signal indicating that the calculation of the rising edge of the waveform has been completed.

 The flip signal shown in Fig. 35 is 0 R, which is the clock that drives the flips 1 66 and 1 70 and the shift rests 1 6 9 and 1 7 4. Since it is obtained from the output of gate 165, it operates only when ACTIV = "1". The flip-flop 1666, the adder 1668 and the shift register 169 constitute the first cumulative adder.

 Input PMO E; ^ 'of adder 1 6 8 Only the first bit time has a logical value of "1" and the other bit times have a logical value of "0". When the eighth bit time, which is the time when the calculation of the tap ends, elapses, the binary number "00000001", that is, the 10-ary number +1 is cumulatively added. Also, when the signal PMONE is all 8 bits "1", "11111111", that is, 1 of 10 decimal numbers is cumulatively added. Therefore, +1 is cumulatively added at steps 0, 1 6, 3 2 and 4 8 and steps 6 4, 8 0, 9 6, 1 1 2, 1 4 4, 1 6 0 1 and 1 are cumulatively added, and steps 1 9 2, 2 0 8 and 2 1 4 are added.

 OMPI

1PO In 2 40, +1 is again added cumulatively. This is almost the same as the change of (R l) _{k in} Table 24.

 The flip 'flop 170, the adder 1 73 and the shift' register 1 7 4 constitute the second cumulative adder. The output 1 7 7 of the first accumulator is applied to one input of AND gate 1 7 2 and simultaneously applied to the other input.

 It is given as an input to adder 1 7 3 under the control of CRY2 signal. Since the CRY 2 signal is a signal that becomes all 8 bit'time "0" in every 16th step, it is prohibited to perform cumulative addition at this step. And

 The CRY 1 signal, which is the input to the AND gates 1 67 and 1 7 1, is the signal that becomes “0” at the first bit time of each step, and each step is the same. At the beginning of the step calculation, the carriage of the previous step stored in the flits: ° · 7 ° 1 ° 6 6 and 1 7 0 is prohibited. The result of the cumulative addition is stored in the shift-restor unit 174, which is latched to the latch circuit 175 (EG, 0 ,. ··-, 7). The clock for the latch is the signal in which CRY1 is synchronized with ARCLK using the OR gate 176.

 The multiplier 20 has the circuit configuration shown in Fig. 36. In this case, the multiplication is performed by the output WG (0,…, 1 1) of the modulated wave generator 1 7 and the envelope generator 1 shown in the signal magnitude guide. Between the ffi force of EG and EG (0… 7).

 In the multiplier shown in Fig. 36, the modulated wave generator 1 7

WIPO Force WG (0, ..., 11) is given to MC <.0., ..., 11), and the output of the envelope generator 19 EG (0, ... , 7) is given to MP (0,…, 7) and the signal ETCK is

 Connected to SYNC.

In this signal ETCK the control signal generator 1 to 5 in the work we are Ru signal, click Lock the number of click MCLK sound 'or scan data over are included in between the teeth ⁰ ls e', which next to Ri if cormorants click lock It is set differently depending on the name, and is set to the number of dichotomy in Table 19. For example, in the case of C sound, it becomes like OUT 2 in Fig. 2-4 (a). This signal ETCK is synchronized once, and the signal ETCK itself calculates the initial value of the counter, register, and 7 ° -flop. It is used for mouth, clear, etc. This multiplier is a typical shift-and-pad / type. Multiplicand is

 1 2 bit Multiplier is set to 8 bits. Therefore, the operation of shift'and 'add will be completed in eight steps, and the multiplication will be completed. Since this multiplier adopts serial type operation, it is possible to add 1 to 2 bit times (1 to 2 master clocks MCLK to drive the multiplier) in one addition. Min) 0 required

 The counter 1 78 and NOR gate 1 92 in Figure 36 are

 1 A binary counter is constructed and a 1-bit ripple key is output to the kneader 1 8 2 for each bit-time. Since one shift-and-ad operation is performed in synchronism with this ripple 'carrier, until the first ripple-key comes out below. To the first step, and then the second ripple '

 OMPI

-WIPO- The process until the exit is called the second step,…, ££.

 The counter 179 is cleared by the signal ETCK. Therefore, seven ripple-carryers of the counter 178 are counted, and a synchronized ripple car is connected to the eighth. Output to the 雳 1 8 3. That is, at the end of the 8th step, the ripple carrier 183 becomes "1".

The ffi force of NOR gate 180 is a signal that becomes "0" every 12 bits when the signal ETCK = ^W 1 ", which is the OR gate 1 8 1 The output of the OR gate 181 is the master clock in the part where the signal ETCK or the ripple ‘carry 182’ changes from “1” to “0”. This signal is a signal whose logic value rises from "0" to "1" in synchronism with the lock MC LK. This signal is the clock of the shift register 1 84. Therefore, the shift register 1 8 4 is initially the signal ETCK and the output EG of the envelope generator 1 9.

 Load (0, 1, 7), and shift one bit at the end of each step.

 The ffi force of the modulated wave generator 17 WG (0, ···-, 1 1), the highest bit (sign bit) WG 0 is the fly: τ ° · flo At 185, the WG (1,…, 1 1) outputs the signal at the shift'resistor 1 86 to the master clock MCLK when the signal ETCK = "1". It is loaded at the start. Also, "0" is simultaneously output to the highest-order bit of the shift maker 186. The output of the shift register 186 is fed back to the input, and then the master output MC

 OMPI

W1PO Every 12 months, a 12-bit time period is set as a cycle. Shift. The output of register 1 186 is the AND gate of the output of shift register 184 for each step.

Control output is performed using 1 8 7. This output is a flip-flop 188, an adder 189 and a shift register.

It is input to the cumulative adder composed of 1 90.

 A partial sum is generated for each step in the shift register 1900. Since this partial sum is fed back from the 11th bit, the partial sum is effectively shifted one bit to the right. Since this shift causes unnecessary data to be returned to the 12th bit'time, use AND gate 191 to prohibit this input. R. In this case, since the number of bits of the multiplier is 8, if the cumulative addition is performed in 8 steps, the multiplication will be completed.

 In this way, the upper 11 bits of the shift-resistor 1 90 and the flip-flop 1 85 are stored. The sine bit will be latched to the latch roadway 195. In this case, the timing of the latch is the same as that of the Ripple'Carry 183 on the Counter 179 and the Master on the Flip Flop 194. · Latched because it is delayed by one bit-time, which is one cycle of the clock MCLK. The data PD (0, ..., 1 1) is given as an input to the DA converter 2 1.

 Next, as a characteristic of the sound wave, a wave having a strong component in a specific area of the frequency waveform and a frequency spectrum that is remarkable.

θΛίΡΙ The synthesis method is described below. Figure 37 shows an example of the waveforms that have the format. Figure 38 shows the frequency spectrum corresponding to this. In Fig. 37, the repetition period of the waveform is T, and the resonance waveform included in one cycle (in the example in the figure, four different amplitudes Inha ⁰ s waveform) c. When the pulse width is taken, the frequency spectrum of this periodic waveform is as shown in Fig. 38 / = T = 4 for the waveform of Fig. 37. Therefore, it has a peak at γ.

Fuhaba value co Size Lee down 'C ⁰ ls e waveform shown in the third Figure _{7, Α 2, A 5, A} 4 is Ru Ah usually to choose monotonous增加or monotonically decreasing. Below, we will describe the method of creating the waveform shown in Fig. 37. The waveform in Fig. 37 is very similar to the function obtained by the two-stage cumulative addition as shown in Fig. 4. Therefore, it is good to create a waveform from the function shown in Fig. 4. Here, as an example, let's take a look at the method of giving a waveform with a frequency of 1 · 2 · 50 Hz with a maximum peak of about 4 kHz. In this example also, the 2 MHz master 'clock is used. For this preparative-out 1 2 5 0 Hz single number of click lock which is Ru contained in the cycle Ru ^{2 X 1 0 6/1 2} 5 0 = 1 6 0 0 Kodea this, the 4 kHz where To create a format in the Wave of loose waveform. Set the width to 0.25 msec. This is 50,000 when converted to the number of clocks.

This step of calculating the ^zero-zero waveform can be done by a two-step cumulative addition of 16 steps.

ΟΛ5ΡΙ The number of clocks is 5 0 0/1 6 = 3 1 2. If we take an integer close to 3.1.25 as the number of clocks, it becomes 3 1. In this case, one co-in'ha in a cumulative addition of 16 steps, including 31 clocks. Ru or al name in the this make Le scan waveform, frequency 1 2 5 0 Hz is the number of the Ru contained in one cycle co Size Lee down 'C ⁰ ls e waveform 1 6 0 0 / (3 1 X 1 6) = 3.23. 3.2 3 over such records, or we integer Ru Oh 3, - three co-Size Lee down Ha ⁰ le scan waveform in the period to summarize the 0 this process ing in and this input Ru The result is as follows. First, the 1600 clock is divided into m = 4 9 intervals, and the number of clocks r _k '(k = 0, 1, 2,… 4 8) contained in each interval is! · (= R =-

Set to 1 1 2. In this state, one step of cumulative addition is calculated for each section. The function used in this case is (R 2) _k , which is shown in Table 13 and Figure 9. As described above, the maximum amplitude value of (R 2) _k obtained by the two-step cumulative addition in Fig. 9 is I (R 0) _k I = C

1 6 CI, proportional to C. And follow the Fuhaba of each of the co-Size Lee emissions' C ⁰ le scan waveform and the child that controls Ri by the C is Ru need der. For example, (R 1) ₀ = (R 2) ₀ = 0, C = 4 (k = 0 to 15),

2 (k = 16 to 3 1) and 1 (k = 3 2 to 4 7) are used to perform two-stage cumulative addition. This is what you get.

The relationship between (R 2) _k and rj is as shown in Table 25, and its waveform is as shown in Figure 31. .. ， ^ 1 ^

 .'cv.Pi

' M II

 Table 25 Table k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

31 31

31 62 93 124 155 186 217 248 279 310 341 372 403 434 465 496 527 558 58

(R2) _k 0 0 4 12 24 40 52 60 64 64 60 52 40 24 12 4 0 0

k 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 .37 rk

 k.

 620 651 682 713 744 775 806 837 868 899 930 961 992 1023 1054 1085 1110 1147 117

L = 0

(R2) _k 6 12 20 26 30 32 32 30 26 20 12 6 2 0 0 1 3 6 Ί

k 38 39 40 41 42 43 44 45 46 47 48

31 112

 k

 ∑ 1209 1240 1271 1302 1333 1364 1395 1426 1457 1488 1600

(R2) _k 13 15 16 16 15 13 10 6 3 1 0

Figures 39 to 41 show the configuration of an embodiment of the musical tone waveform generator having a font. The nonwoven Le Mas emissions acquired waveform Ri Oh fourth 2 diagram (a) the indicated such waveforms, Toku徵of scan Bae click preparative Le of its is Ru contained in one cycle co Size Lee down Ha ⁰ It is known that it depends on the number of notches and the amplitude and the amplitude. In addition, it is a well-known fact in the field of speech research that the transition from one vowel to another vowel has a'continuous transition 'of the fomant frequency. Be appreciated.

In an embodiment of this view of the fact this co Size Lee emissions * C ⁰ ls e of Ru determined the full O Le Mas down bets frequency width of the (first 4 r of FIG. 2 (a)) and nonwovens, Le Mas down bets width vibration that determines the shape _{(AQ, Α 1, Α 2} , ...) to be devised to cormorants by Ru given the time change Les, Ru. In this example, the concept of (repetitive waveform) X (envelope waveform) used in conventional musical tone waveform generation is removed, and the time point of generating the repeated waveform is eliminated. By controlling the amplitude, the hardware is being labor-saving.

Figure 39 shows the ROM that stores the data that determines the shape of the waveform. Note Li MEM 1 3 * 2 3 7 is co-Size Lee emissions are included in one period of the waveform. C ⁰ of eyes Ru given the number of Le vinegar of the Ru Oh. Vinegar and :) is the cumulative addition scan STEP and the number of each each tooth ⁰ le scan width of'm lever co-Size Lee emissions' C ⁰ le scan to this invention (the fourth FIG. 2 (a) Te Tsu It is determined by the number of master blocks included in the group. Memory MEM 1 4 · 2 3 8 is one co-in'ha. This is to give the number of steps to generate the loss. In other words, ST 2 5 6 is "1" for the 2 5 6 step.

f OMPI W1FO In the case of 1 2 8 steps, ST 1.2 becomes “1”,…, and in the case of 1 6 steps, S Τ 16 becomes “1”. The number of master clocks included in each step is stored in memory MEM 9 * 233 and memory MEM 10-234. In this case, the memory MEM 9-233 gives the initial value and the memory MEM 10-234 gives the final value.

The transition of the normal frequency is obtained by shifting the number of master clocks included in each step from the initial value to the final value. Co Size Lee down 'C ⁰ ls e of Fuhaba value here (A ₀ of the 4 2 Figure _{(a),, A 2,} ...) is also of a to decrease monotonically, A _k = A ₀ r We satisfy ^k . Here, r is the damping ratio of the amplitude and is stored in memory MEM 11 -235 and memory MEM 12 · 236.

 In this case, the memory MEM 11-235 gives the initial decay rate, and the memory MEM 12-236 gives the final decay rate. Memories MEM 9-233 to Memories MEM 14-238 select output according to TC (0, ..., 3), 0 C (0, 1, 2) and VC (0, 1, 2,). Be touched. Here, V C (0, 1, 2) is a 3-bit address, which corresponds to 8 tones. The data given to memory MEM 9-233, memory MEM 10 * 234 and memory MEM 13.237 are negative numbers (2's complement display).

 Although Fig. 40 shows the circuit configuration of the control section of the waveform waveform generator, it has a similar configuration to the circuit of the control signal generator shown in Fig. 21. Flip 'Flop 2 3

: O. PI 1 .. Synchronize the KEY signal to the master 'clock MC.LK'. Flip-Flip: From the Q-terminal output signal of 7 ° 2 3 9 further differentiated by the Flip-Flop 2 4 0 and NAND Gate 2 4 1. I CLR is created by the circuit. The CPTCK output from the AND gate 251 is a signal that is synchronized with each step of cumulative addition. CPTCK and I CLR are inputs to NAND gate 2 4 2 and produce CPSTP.

 Every time the CPSTP becomes "Γ", "EDCBA" = "0 1 1 0 0" is loaded in the counter 1 2 3 4 o Therefore, the data is loaded. After that, if the master clock is counted 19 times, a ripple carrier will occur. The output of the NAND gate 2 4 4 is a signal that rises to the 20th count of the falling edge of the ripple carrier. Therefore, the flip-flops 2 4 5 must be reset by the CPSTP.

20. It will be set after a clock. The output of the NAND gate 246 is a clock signal including 20 master clock π-ck MCLK after counting CPSTP.

 The number of clock counters — 2 4 7 determines the number of master clocks MCLK included in one step of cumulative addition. The value NCKF is counted with RCLK 4 and the intermediate value is given to the module X counter 1 2 4 8. The Modulo-X counter 2 48 is the output of NOR gate 2 49, that is, I CLR or CRY (the counter of Fig. 21 1). 1 1 3 5 output). Therefore, the output OUT 1 is MC K for each count of the number given to input X.

O Pl A cycle of "1" is generated for one cycle.

 —Flip flip 'The output Q of the flip 250 is 0 AND gate 2 5 which is 1 "by I CLR or F CRY and then" 0 "by CPCRY. The output of 1 is CPTCK: The output is 1 when the output Q of the τ ° -flop 250 is "1" and the output OUT 1 of the X-counter 2 4 8 Therefore, when Q is "0", it is a signal whose logical value is "0".

 CPTCK is input to the enable terminal (EN) of the counter 2 53. The input of the counter 2 5 3 is S T 1 28,

ST 64, ST 32, 3 1 ^> 16 and 0 11 Gate 2 5 4 speaks according to ^) 0

When ST 1 6 = "1", "DCBA" = "1 1 1 1", ST 3 2 = ^w 1 "When DCBA" = "1 1 1 0", ST 6 4 = ".1 When it says "DCBA 1 1 0 0",

When ST 1 28 = "1", "DCBA" = "1 0 0 0", and when ST 256-"1", "DCBA" = "0 0 0 0" becomes the input data. . Therefore, the NOR gate 2 52 and the counter 2 5 3 output the ripple key each time CPTCK comes when ST 1 6 = "1", ST 3 2 = "1" once every 2 times, ST 6 4 = "1" once every 4 times, ST 1 28 = "1" once every 8 times , ST 256 = ^W 1 "apply the ripple carrier once every 16 times.

 This ripple 'carrier is further counted by a 4-bit binary counter 2 5 5 and outputs a ripple-carry NPLS. Suru. This NPLS is

Ο. \: ΡΙ It is a signal to go out. For example, when ST 6 4 ϊ '"is a count counter 2 5 3, the ripple' carriage is output when four CPTC counts are output, and the count is output. One 2 5 5 ripple carrier — NPLS outputs when counting 4 X 1 6 = 6 4 CPTCKs.

The output CMPL of the one-cycle 0 R-, ... 3 NPLS used to take the 2's complement of the initial value that is a signal that becomes "1" in the middle two intervals and is used for cumulative addition by equally dividing the loss into four intervals. Is the 0R gate 258 and is logically ORed with FCYC (the output of NAND gate 137 in Figure 21) to form the INPLS signal. The counter 1 ² 5 7 is a negative sign (2's complement).

Number of pulses NCP is loaded, NPLS is counted, and ripple carrier CPCRY is output. O CPCRY is the end of calculation of the node'north. It is a signal that indicates this. First

 The timing diagram of the main signals in the circuit of Figure 40 is shown in Figure 42 (b).

^ This is ¾ 5 0,

 Figure 4 1 is a circuit diagram of the part that applies to the waveform generator of the fo- mant waveform generator. The engine power counter — 2 5 9 counts from the initial attenuation rate ARI to the final attenuation rate ARF with the clock RCLK 5 and the intermediate value ART (0,…, 7). Is output. This is connected to M P (0,…, 7) of the multiplier 260 (detailed circuit diagram is shown in Fig. 36). On the other hand, the output EG (0, ..., 7) of the envelope generator 19 is repeated by FC YC at the beginning of one cycle of the repeated waveform, and the raster circuit 2 61 is connected to the latch circuit 2 61. "

O.MPI It is checked. This is the first course :. -It is equivalent to the amplitude of the loose. This signal is applied to the A input of the selector 1 262. The flip-flop 2 6 4 is reset at the beginning of one cycle; the logical value of the ffi force Q is 0 ", so the signal is zero. Since it is connected to the select terminal s of the connector 162, the A input is selected as AMP (0,…, 7) at the beginning of the first trimester. AMP (0, ··· ,, 7) is connected to MC (1, ····, 8) of the multiplier 260. (In this case, MC 0 and MC (9, 1 0, 1 1). ) Is "0".) Therefore, 8 bits of PD (1, ..., 8) of .12 bits output PD (0, ..., 1 1) of the multiplier are latched. Chi circuit 263

The latch circuit 2 6 3 latches PD (1,…, 8) with NPLS, and the flip-flop, Q of the liner 2 6 4 is a logical value at the rising edge of NPLS. 1 "the second co-support Do that's in the stomach down Ha ⁰ Norre is a Fuhaba value of the scan PD (1, ..., 8) is of Selector Selector Turn-2 6 2 ffi force AMP ( 0, ...--, 7). This PD (1, ..., 8) is the amplitude value of the first cousin hall multiplied by ART (0, ..., 7). And follow AMP (0, -, 7) is one mosquito window down the door to every you (co Size Lee down Ha ⁰ Le vinegar every you one month window down door.) ART double the NPLS This means that the amplitude attenuates exponentially.

 The AMP thus obtained is loaded in parallel to the shift resister 2 65 and output in series.

f 'O PI 2 6 7, Impactor 2 6 6,, 'J —.K 7 U 7 ° hoop π 2 6 8 and selector 1 2 6 9 compose a 2's complementer. AND GATE 2 6 7 input C MP L II: Take "2" complement when "1". The output of the selector 1 2 6 9 is adjusted to the amplitude using the shift register 2 7 0 and the AND 0 0R gate 2 7 1 and sent to the cumulative adder. It is. Flip 'Flop 2 72, Adder 2 7 3, Shift'Register 1 2 7 4 constitutes the first cumulative adder and the flip' Flop 7 ° 2 7 5, the adder 276, and the shift register 1 27.7 constitute the second cumulative adder. The output of the shift register 2 7 7 is latched by the latch circuit 278 and fed to the D / A converter 2 7 9.

 As described above in detail, according to the method for creating a function by cumulative addition of the present invention, the apparatus for creating a function, and the method for creating a tone waveform using the same, a method of cumulative addition is used as a basis. Then, it is possible to generate various sound waves, which are various functions and their applications. Based on the basics of cumulative addition, the calculation process is simple, the device configuration is not complicated, and various functions and musical tone waveforms with desired accuracy can be easily created with high accuracy. You can do it.

_ ΟΛΊΡΙ Roh ^'Wl °

Claims

Request range ffl:

1. Let X be any real number, and let k = 0, 1, 2, ... Polynomial ( _X ) = — a _Q + a _{l X} ¹ + a ₂ x for evenly spaced discrete values X = k X of variable X ² +-+ a _N x ^N , (: a _N ^ 0, N = l, 2, 3… :) The value / (kX) is calculated sequentially with respect to the step variable k. +1 register β 0 to RN and at least one adder are provided, and the value of the first coefficient C is cumulatively added to the register R 1, (RN) _k Is the content of the _k step of the register RN, and using the coefficients a ₀ , a, a ₂ "-a _N of the polynomial expression / (X), (RN) _k = / (kX) The first coefficient C and the initial value (R1) Q to (: RN) Q calculated to satisfy the above are set to the registers R 0 to! N, respectively, and (Rl) _{k + 1} = (Rl) _k + C, (R2) _{k + 1} = (R2) _k + (R1) _k , (R3) _{k + 1} = (R3) _k + (R2) _k …

Cumulative addition of (RN) _{k +} = (RN) _k + (RN— l) _k 'is performed using the adder described above, and at the kth step, the value of the register RN is (11 ^) ₁ ^. A method of calculating an Nth degree polynomial whose characteristic is to obtain the cumulative addition value ().

2. Let X be any real number and let k = 0, 1, 2, ... Polynomial ^ (x) = a _C) + a ₁ x ¹ + a for uniformly spaced discrete values x = k X of variable _{X In} a device that sequentially calculates the value (kX) of ₂ x ² + "'~ f- a _N x, (a _N = ^ 0, Ν = 1, 2, 3, 3…) for the step variable k , The contents of the register of the previous stage and the contents of the register of this stage are added by the adder, and the cumulative stage that sets to the register of the relevant stage continues for multiple stages. The cumulative addition means and the stage where the first stage coefficient c is set as the input of the previous stage of the accumulator, and (R Ν) at the start of the calculation. As the contents of k step of RN, the calculation interval X and the coefficients a ₀ , _{& 1} , a ₂ … a _N of the polynomial / (X) are used, (RN) _k = / (k X)) and the first coefficient C calculated so as to satisfy X) and the initial value of the register of each accumulator are stored in the corresponding register. A polynomial computing device with and.

3. At least one interval containing at least one step is used to form a large interval, where N is an integer greater than or equal to 1 and there are N + 1 register R. 0 ′ to RN and at least one adder are provided, the first coefficient C and (R i) _Q to (RN) at the starter R 0 to 11 1 ^ at the beginning of the large section. And set k = 0, 1, 2, 2… for each step.

(R l) _{k + 1} = (RD _k + C, (R 2) _{k + 1} = (R 2) _k + (R l) _k

(R 3) _{k + 1} = (R 3) _k + (R 2) _k … (RN) _{k + 1} = (RN) _k tens-(RN-l ^ Performs cumulative addition of polynomials and the second interval At the beginning of each subsequent section, change the first coefficient C and at least one of (R 1) _Q to (HN) 0, and perform the cumulative addition with the step polynomial. Is performed, and register R 1 ~

 A method of calculating a polynomial whose characteristic is to obtain a function in R N.

4. In the method described in claim 3, the large section is composed of first and second sections, and the number of steps included in each section is n (n = l ,. 2, 3,4, ...), the first coefficient C is 1 C in the first section, and _ in the second section: _

ΟΛ ', ΡΙ , And the above (RD Q, (R2) o, (R3) ο… are respectively yn C, -n C, (n-η C, (-gen n + _n "C…), and A method of calculating a polynomial whose characteristic is to obtain an in-function and an approximate cos-in function.

5. The method according to claim 3, wherein the large section is composed of first to fourth sections, and the first coefficient C is + C in the first section and the fourth section. 2 and 1 C in the third section]), and (Rl) ₀ , (R2) ₀ , (R3) ₀ , ( ² C,-

A method of computing polynomials, which is characterized by obtaining numbers and approximate cosine functions 0

6. In the method according to claim 4 or 5, according to the first coefficient C and the number of steps n]? An approximate sin function whose maximum amplitude is determined is also preferable. Is the portion corresponding to one cycle, half cycle, or ^ "cycle of the approximate cosine function, and differs by at least one of the first coefficient C and the number of steps _n. A method of calculating a polynomial whose characteristic is that a function obtained by connecting the above functions with different values in time is defined as one period.

 7. In the calculation method described in claim 3, a small step is created by equally dividing the steps described above.

(RN) ₀ is maintained as it is and the first coefficient C and the above

(R1) (R2) (RN-1). To 1 /

 OMPI

"WIPO Cumulative addition to the cluster RN is the above-mentioned small step. Steps: Every 7 °. The cumulative addition to the registers R l, R 2, ... to RN-1 is k = 1, 2, 3…. Then, a method of calculating a polynomial characterized by performing intermittently only on the k-th step.

8. The method of calculating a polynomial according to claim 1, which is characterized in that each cumulative addition of a plurality of polynomials is performed using one set of multistage cumulative adders.

9- In the calculation method described in claim 3, when the function is obtained by cumulative addition of a large section, the calculation cycle of each section may be changed by keeping the repetition cycle constant. The reason is that the repetition cycle is changed]? A polynomial operation is performed to obtain a function in the registers R 1 to RN. A polynomial calculation method.

10. In the calculation method as set forth in claim .9, the number of T master blocks is 7 m for each step S r _k (k = 0, 1, 2 - m -. 1) Ma is te one click Lock divided into cormorants'll contain the phrase, value rj = r _k + q _k number of the q _k and the summing of the value of this r _k The master clock of m-1 m-1 m-1 m-1

 ∑ rk '-T and a polynomial equation characterized by the fact that k = ok = o "k = ok = 0 that satisfies ∑ ∑ rk + ∑ ¾k is included in each step. Method of calculation.

11. In the calculation method described in claim 9, the clock obtained by dividing the master clock containing the highest required octave is calculated. Lock ^

 OMPI

, The — A method of calculating a polynomial expression that is characterized by performing an operation.

 12. In the calculation method described in claim 9, a master polynomial is characterized by dividing a master clock into a required value and generating a waveform having a pitch of equal temperament. Method of calculation.

 13. In the calculation method described in claim 3, the cumulative addition of each step at the beginning of the large section is the target rise of the musical tone waveform. It is performed in synchronism with the clock that is proportional to the speed of, and the cumulative addition for each step is performed at the end i? A method of creating a musical tone waveform that is characterized in that it is performed in synchronism with the clock proportional to the speed to obtain the waveform of the envelope.

 14. The method of claim 13 in which the method of forming a musical tone waveform is characterized in that, in the process of calculation, it has at least one section in which the calculation of cumulative addition is stopped.

 15. In the calculation method described in claim 13, the value of the first coefficient C may be increased or decreased in accordance with the rising and falling of the musical sound waveform for each large section]). A method of creating musical tone waveforms, which is characterized by decreasing and changing the envelope of the waveform.

16. According to the scope of claim 13]? The obtained envelope waveform and according to the scope of claim 12] 3 are integrated and the waveform having the equal temperament interval is integrated. To form a waveform 5. How to create a sound waveform.

7. The approximate number of sinusoidal functions obtained from claim 3 or the number of waveforms included in one cycle of the approximate cosine function, the amplitude, and the c. A method of creating a musical tone waveform, which is characterized in that it is possible to create a waveform of a normal by controlling at least one of the pulse widths.