JPH0289109A - Sine wave generation circuit - Google Patents

Abstract

PURPOSE:To improve the precision of a sine waveform irrespective of the size of ROM by storing data in a form that a numeric operation is added to sine wave data in an address component. CONSTITUTION:Data obtained by subtracting the value of a triangle wave for address from sine wave data corresponding to triangle wave data for address is written into ROM 13. (N) bits of triangle wave data from an absolute value circuit 8 are held by a register 14 as they are, and high-order (m) bits which are obtained by removing the highest-order bit and subsequent-order bit from (n) bits are divided, whereby divided (m) bits are inputted to ROM 13 as address data. An addition circuit 15 decimates an output which is obtained by adding triangle wave data of (n) bits to output data of ROM 13. Thus, the sine wave whose relation of a ROM capacity and the precision of the sine wave is improved can be generated.

Description

DETAILED DESCRIPTION OF THE INVENTION [Part 1 of the Invention (Industrial Application Field) This invention relates to an improvement of a sine wave generation circuit that uses a ROM (to generate a sine wave).

(Prior art) A sine wave generation circuit that obtains a sine waveform by filling a readout W memory with one sine wave 1 data in a ROM and inputting time axis data based on a sawtooth wave as an address. There is.

FIG. 7 is a block diagram showing an example of the above-mentioned sine wave valve circuit. Added g7
Input to circuit 1. Depending on the value of this C)J
It is possible to determine the frequency of the sine wave.

The addition circuit 1 and the 7-key 1-mulator type register 2 constitute a sawtooth wave generation circuit 3, which cumulatively adds the input C(i) L/
'(Outputs sawtooth wave data. However, addition ζ) The output data of circuit 1 is divided into n bits (n is an integer) data and 16,
The output data of the sawtooth wave generation circuit 3 is the output data of the sawtooth wave generation circuit 3. Sawtooth wave data hζ is output by truncating 1Z-order nm bits from the wave data.

-F Note [The n-bit sawtooth wave data becomes address data (') and is input to ROM 4. In ROM 4, sine wave data is written in correspondence with the address data -C, and -Fi (j m Every time the highest bit of the bit sawtooth wave data changes due to digit F, the ROM
4 outputs sine wave data corresponding to each address.

Figure 8 shows the circuit of Figure 7! 11J is a waveform diagram shown in a 7-thick [lg] format, (a) shows the analog waveform of the sawtooth wave output from the sawtooth wave generation circuit 3, and (b) shows the analog waveform of the sawtooth wave output from the sawtooth wave generation circuit 3. The analog waveform of the output 4 sine wave data (each shown is -1°).
It is normalized to "1", and one cycle of the sawtooth wave corresponds to one cycle of the rein wave.

When attempting to generate a high v1U sine wave using such a circuit, n=m is set and all n pins 1 to 1 are used as address gaters for ROM/l. Therefore, if you try to improve the precision of the -C1 sine wave, the ROM capacity will become smaller, which is not convenient.

Figure 9 shows another conventional circuit in which the ROM It size is reduced to 1/1 by utilizing the symmetry of the sine wave. This constitutes circuit 3. However, the number of output bits matches the output pins 1 to n of the adder i circuit 1. The absolute value of this sawtooth wave data of n pi 1~ is taken by the absolute value circuit 5, and the absolute ID circuit 5 outputs triangular wave data in which the negative side of the sawtooth wave is folded to 1 from the center value. Subsequently, the addition C) circuit 6 applies a standard value to the triangular wave f-ta from the absolute value circuit 5.
0.5" is added. This causes the addition circuit 6 to
The DC component of the triangular wave data outputted by the value circuit 5 is downshifted, and triangular wave data whose positive and negative half cycles are determined is output. This triangular wave data i, the amplitude is +II Q, 5
It is n-bit data in the range of II to −”0.5°.

Next, the triangular wave data to the [) pin 1 is input to the register 7 and the absolute value circuit 8, respectively. The absolute circuit 8 is
10"0.5°・～--゛0.5°; The triangular wave data in the mountains was converted into an absolute value and C1"o"~to°"0.5
” outputs triangular wave data in the range 7 dress data of ROM9. In this case, the output triangular wave data consists of the most significant 0)) bit and the next -F (R7 bit l- of ◇). , j: manually input the m bits into the ROM 9 as a data.

The sine wave switch t, 1 is stored in ROM 9.
．． Sine wave data for 0.~F/2 (radian) division
(・Yes.Previous 1.L! Absolutely triangular wave from j value circuit 8)
-Evening is "O"'~+'0.5' and '0.5'~II
The repetition of OIT's block [] - block produces a sine wave of O~π/
2. This corresponds to π/2/π, and as a result, the ROM 9 outputs a sine wave arc corresponding to the half-circumference of iF of the sine wave. This sine wave data (,1, becomes one input of the east circuit 10.

On the other hand, since the data temporarily held in the register 7 is a triangular wave with a negative polarity f of 1 added, this sign data is judged by the sign judgment circuit 11. It is possible to determine J. That is, the switch 12 is turned off by the above-mentioned discrimination output.
L, when the discrimination output accepts a positive half cycle, the code is cut off H
Switch f12 indicates x1. Multiply n circuit 1 by multiplying data
By setting the other input to 0, the positive half-circumference of the sine wave is obtained at the output of the multiplication circuit 10. In addition, when the discrimination output decreases the negative half cycle, the sign changeover switch 12 changes X(-)1 to the other input of the circuit 10 and As a result, the half-circumference of the sine wave [A] is obtained at the output of the circuit 10.

FIG. 10 is a waveform diagram (a) which schematically shows the operation of the circuit shown in FIG. 9. al, , shows the waveform based on the output data of the L-saw + 'Ja-shaped wave generation circuit 3, and b is the waveform of the absolute wave generator 5.
C is the waveform based on the output data of the addition circuit 6, d is the absolute waveform based on the output data of the circuit 8, e is the waveform based on the output data of the ROM 9, f is the multiplication peak Waveforms based on output data of the circuit 10 are shown respectively.

As can be seen from each waveform a to d, by processing the sawtooth wave data a in the order of the absolute value circuit 5, the tightening circuit 6, and the absolute value circuit 8, the triangular wave data d, which becomes the address data of the ROM 9, is This becomes a triangular wave with twice the frequency of the sawtooth wave data a output from the wave generating circuit 3. For a triangular wave with such a frequency, one triangular wave section of A corresponds to one half cycle of the output sine wave, so it further corresponds to one slope section of the output sine wave. ROM9
By inputting triangular wave data continuously, we can obtain a sine wave with only the negative half periods lined up, and furthermore, by inverting the polarity, we can obtain a sine wave with the negative half period folded back to the correct 0 side. You can get C.

However, in such a sine wave generation method (also, ROM
9 is given an address in which the lower bits have been truncated, a hanging error occurs, and as a result, a correct sine wave amplitude value cannot be obtained.

FIG. 11 is an explanatory diagram of converting the amplitude error from the quantization error, in which the horizontal axis indicates the 7dress data to the ROM 9, and ta@ indicates the output data of the ROM 9, respectively. X indicates the address of a sampling point before truncation (l'1), X' indicates the address after truncation < r (fi, the address corresponding to J (+
Indicates Q. Further, Y indicates the J sine wave amplitude value corresponding to X, and indicates the IY sine wave imaging width value corresponding to Y'G and LX'.

The keratinization value Δχ is Δx == X −X'<, 2-Ill・(1)
becomes. The quantization error of X is the error Δy as a sine wave
This will be converted to the following equation.

Δ y=sin (xx) −5in (!
X' ) One cos (Animal X)・Δχ
...(2) (Problem to be solved by the invention) In the conventional sine wave generation circuit 1 using ROM, although there is a proportional relationship between the size of the IX conversion step and the sine wave amplitude error, When placing the =Q point on the ROM lease, I left out the setting ↑ with the viscosity of the sine waveform set to 1λ11.

This invention eliminates the above problems and provides a sinusoidal waveform of
The proportional relationship with the M size has been improved, and the sine waveform has been improved in comparison to the conventional ROM size! The purpose is to provide a sine wave generation circuit that allows you to use τ! 76゜ [Structure of the Invention] (Means for Solving the Problems) This invention uses a ROM to generate a sine wave using J5 in a circuit that generates a sine wave, and generates sawtooth wave data corresponding to a predetermined period of the sine wave. Convert the data into four-axis data, cut off the specified pits of this 11-axis data, and convert the data to 1'? 7 address data to the OM, corresponding to the address data of the mouth, 11
The input data is in the form of a mathematical expression of the address data and sine wave data, and the read output is subjected to the inverse operation of the mathematical 0 with the sawtooth wave data to obtain a sine wave. It is characterized by doing something like this.

(Function) Generally, in a sine wave generation circuit using ROM, RO
The sine wave data stored in M includes an address component, which is time axis data, in its amplitude data. This invention provides mathematical ζi for the sinusoidal data component in the address component.
A nohuta in the form of adding jf';'i is stored in the ROM. Therefore, real! Since a filter that does not include the address component is stored, the amplitude error caused by the termination error λ is reduced accordingly.

(Example) Hereinafter, this invention will be explained by referring to the illustrated example.
I will clarify.

FIG. 1 is a circuit diagram e showing one embodiment of a sine wave generating circuit according to the present invention.

In FIG. 1, the same elements as in FIG. 9 are designated by the same reference numerals.The human power C" which determines the frequency of the M0 sine wave is composed of a shearer I and a resistor 2 in synchronization with the lean-bring period. Sawtooth wave generation (L- Input to circuit 3 and output as sawtooth wave data whose value increases with a predetermined slope.The amplitude of this sawtooth wave data μ') bits (n is a positive integer) “Shi”
1", the absolute value circuit 5 returns the negative half period of the sawtooth wave data to the IF side, and the amplitude is II OI.
Triangular wave data of T~+°゛1°° is generated. This triangular wave data is input manually to the circuit 6. The tightening circuit 6 adds -゛1'' to the input triangular wave data.
From the circuit 6, a triangular waveform generator 7-1 with t, L and amplitude 511 is output. The number of output bits of the addition ( ) circuit 6 is n
It is.

Next, the output of the addition circuit 6 (Y) is input to the 1-value circuit 8 and the register 7. The absolute value circuit 8 folds the negative half period of the data from the addition circuit 6 into the positive side. Return: The triangular wave based on this data has twice the frequency of the sawtooth wave output from the sawtooth wave generation circuit 3, and has an amplitude of 1101T to II Q.
, 511. "Repeat 0.5°" to II O11.

Conclusion: The double frequency triangular wave data from the 1-value circuit 8 is n
The bits are held as they are in the register 14, and the most significant bit and the next most significant bit are removed from the n bits (9m bits (m is a positive value smaller than n-2)) are distributed. The reason why the F-order 2 bits are removed is that the present invention uses the ROM 13 as data for generating a sine wave, and only occupies the O~π/'2 interval using the S-1 symmetry of the wave-sine wave. It's for a reason.

Minute? 11j m bits 4. Input to iROM 13 as address data. In other words, the address triangular wave data input to the ROM 13 is input to the ROM 13 and consists of n bits with amplitudes of 110 to 110. It is data.

Therefore, the ROM 13 contains data obtained by subtracting the value of the triangular wave data for address from the ◆9 wave data corresponding to the triangular wave data for address (-). The output data of ROM13 due to this is +111 &'2
One side of the circuit 15 is output as human power. On the other hand, the register 14 supplies n-bit triangular wave data to the other side of the addition n circuit 15 in accordance with the output timing of the ROM 13. In this way, the addition circuit 15 adds n-bit triangular wave data to the output data of the ROM 13 and derives an output. The output data of this adder circuit 15 becomes sine wave data in which positive half cycles are arranged. Then, the sine wave data from the control circuit 15 is passed through a determination circuit 11 (the polarity of which is determined by a switch 12) which determines the sign of the output of the register 7
The output data "1°, -" OII is converted into a sine wave f-ta having a polarity sign of 1 and 1 by the output circuit 10.

One embodiment of the present invention is constructed as described above, and its operation will now be explained with reference to the second factor and FIG.

Sawtooth wave generation circuit 3. Absolute detective circuit 5. Addition circuit 6 and about 1=+value circuit 8? )> The circuit is the same as the circuit in Figure 9, and is shown in Figure 10 a-d.
explained in.

Figure 2 shows the operation of the circuits subsequent to the absolute circuit 8.
There are waveform diagrams, d is absolute (the waveform from the output γ-ta of the 1r1 circuit 8, e' is the output data of the ROM 13, e is the output data of the adder circuit 15, and the waveform from the rμ multiplier circuit 10 output data). are each small.

According to this embodiment, the data e' stored in the ROM 13 consists only of data corresponding to 1/4 section of the sine wave. The address triangular wave j'-ta (j has one slope section corresponding to 1/4 section of the sine wave) of the absolute square circuit 8, and the data e' is It will be read out corresponding to the 1/4 section.

FIG. 3 is a β1 diagram schematically showing the relationship between the data e' written in the ROM 13 and the address triangular wave data (j and correct input wave data F.
．． L/' represents the address on the triangular wave i-ta for dressing, and the vertical axis represents the sine wave arc.

Now, when the n-bit 1 digit of the absolute λ/1-value circuit 8 receives the value XI, the address triangular wave data Mi is
' and? 1, the ROM 13 outputs the data of the corresponding point 01 in l'J and data e' by X'. The data for the 01 point in each case is given by sin (X') -X''Q.

On the other hand, from the register 14, the 7th address (10X is the output -J6゜this X
When converted into n-bit triangular wave data, the value is shifted by 61 minutes from X' (there are 11 points of data C. Addition circuit 1
5 adds the data of these 61 points and the data of 01 points.
Data e outputted from C1 and 1.1 circuit 15
is sin (X') -X' 1X, and f
Represented by 1 fish.

In this way, when data similar to the 11 points is applied to the last number 1q of the m-bit address triangular wave data d, a sine wave with positive cycles + 111 arranged as shown in e is formed, and the changeover is performed by the changeover switch 12. Accordingly, it is possible to create a sine wave as shown in (, [). Such sine wave data is
By adding the correct address to the data e' read out using the address X having a quantization error, a sine wave with a higher amplitude than before is obtained as described below.

The sine wave obtained by the above embodiment and the sine wave obtained by the circuit shown in FIG. 9 will be discussed.

First, the amplitude error of the sine wave obtained by the circuit of FIG. 9 due to the negative seven error is expressed by equation (2). From this, if we sieve the error energy, on the other hand, if we find the error energy V- of the sine wave obtained by 19 from the circuit of FIG.
The quantization error Δχ is expressed by equation (1) as in the case of FIG.

If the amplitude data corresponding to 11 points is written as Y rr, then Δy
= y −y ″= 5in(X)−(sin(X'
)-X')-X= stn(Z' x)-stn(-p
x')-(x-x')...(4) From the above equation, Δy is π Δy metacos(-X)・Δ''-Δ1 π...(5) From this, the error energy is (6 ) and (3), 101 og(Pe1/Pea) = −7,23[(
jb]...(7). Therefore, the circuit of FIG. 1 has better sine wave accuracy, ie, S,/N, than the circuit of FIG.

Next, another embodiment will be described.

FIG. 4 shows another embodiment of the invention, in which the same elements as in FIG. 1 are given the same reference numerals. The configurations of this circuit (1, sawtooth wave generating circuit 3, absolute value circuit 5, and adder circuit 6 are the same).The output of the adjustment circuit 6 is input to the absolute value circuit 8 and the register 7, respectively. The absolute value circuit 8 converts the n-bit triangular wave data into m bits and supplies it to the ROM 16 as address triangular wave data.

In the ROM 16 of this embodiment, data obtained by converting address triangular wave data into a sine wave is further divided by address triangular wave data.

The output of the ROM 16 is connected to the r1 bit data from the register 7 and the east exit circuit 17, and the fraud circuit 17
Outputs a sine wave with more positive half periods lined up.

On the other hand, the output data of the register 7 is transmitted to the sign discrimination circuit 11'
c is determined, and the changeover switch 12 is controlled based on the determination. The sine wave data from the east exit circuit 11 is sent to the multiplication circuit 10'c switch 71 as in the case of the circuit shown in FIG.
It is multiplied by the polarity switching data "I IT ll 1" from 2 and becomes sine wave data.

FIG. 5 shows the operation of the circuit in FIG. 4, where d is the absolute value circuit 8.
C″ represents the waveform based on the output data of the ROM 16, C″ represents the output data from the east exit circuit 11, and f represents the waveform based on the output data from the east exit circuit 10.

The data for sine wave generation written in the ROM 16 is expressed as sin (X'), where X' is the triangular wave data.
The waveform e'' is a sine wave with a subtracted vibration that subtracts the characteristic C of the block in the triangular wave data d.To be precise, Since the section corresponds to 1/4 period of the sine wave, -1 is included for the subtraction vibration curve of 1/4 period of the sine wave.

Thus, the output 16 damped vibration curve t from the ROM 16 is offset from the correct data X and I) from the register 7.

This corresponds to the mathematical operation performed by the adder circuit 15 in FIG. 1, and can be schematically illustrated as shown in FIG. 6. In Figure 6, the horizontal axis represents the address axis, and the vertical axis (,
1 sine wave amplitude data, i26 is triangular wave data for addressing in ROM 16, F is a true sine wave, and e'' is a damped vibration curve that enters and exits ROM 16. The data at e'' is represented by point e2, and the data at e2 is multiplied by the triangular wave data at d2 corresponding to the correct address is obtained.The data at point f2 is sin (X'), X
...(8) Represented by X'.

Next, I will explain that the precision of the sine wave can be improved by such mathematical manipulation. For convenience of explanation, RO
The data stored in M16 is s+n (-X'), /
Take X'.

“Amplitude data Y IJ at two points is obtained from equation (8).

Therefore, the amplitude error △y is (fish x) - and -5in (fish x') Δy = s"02
X・2 Error energy pe is pe2−Δχ2 flΔy”dx=0.50Δx2−(
11) Comparing this with the case in Figure 9, we get 10-M oo(Pe2 /peO) --3,9[dBl...(1
2), and the sine wave error is J in the case of Fig. 9, 3.9 [
How little dBl works. On the contrary, in order to obtain a sine wave of the same viscosity, the address bit is reduced by approximately one bit, and the capacity of ROM+6 can be halved.

In addition, in the example shown in Fig. 4, there are 3 ROM tables) (animal X)
/ (=x>. This is to make the function value smaller than ``1'', and since the value of X, that is, the value of register 7, is a triangular wave in the range of ±II Q, 511, The amplitude value of the output sine wave is 10""Y" - ±0.31
The range is 8. If necessary, add a coefficient π to the output i) I
J is fine.

As described above, the sine wave generating circuit according to the present invention has a ROM
Then, as the data to be stored in 11, the sine wave is modified by 7 dresses and 0 in mathematics, and when it is read from the ROM, the correct address is 21!・Inner oil ζ
) by performing the inverse of Q and outputting the sine wave component, (1
It is possible to obtain a sine wave with less error (1 channel) caused by quantization error. For this reason, the same capacity R as before
OMr, u1maro's roaring sine wave! '7 can be done. Conversely, it is also possible to reduce the capacity of the ROM and generate a sine wave of the same magnitude (i).

C Effect of the Invention 1 As explained above, according to the present invention, it is possible to generate a sine wave in which the relationship between the ROM capacity i1 and the sine wave viscosity is revised by one rank.

[Brief explanation of the drawing]

FIG. 1 is a circuit diagram showing an embodiment of the sine wave generating circuit according to the present invention, FIG. 2 is an operation waveform diagram explaining the operation of the circuit in FIG. 1, and FIG. FIG. 4 is a circuit diagram showing an embodiment of the present invention; FIG. 5 is an operation waveform diagram explaining the operation of the circuit in FIG. 4; FIG. According to the embodiment of the figure, 11 - An explanatory diagram of the output process of a string wave, Fig. 7 is a circuit diagram of a conventional sine wave light circuit, and Fig. 8 is a circuit diagram of a conventional sine wave light circuit. 9 is a circuit diagram showing another conventional circuit, FIG. 10 is an ε waveform diagram explaining the operation of FIG. 9, and FIG. 11 is an explanatory diagram for converting the amplitude error from the fl quantization error c1. 1...hu 0 circuit, 2...register, 3...sawtooth wave generation circuit, 5...absolute value circuit, 6...addition → circuit, 7...register, 8 ...Absolute value circuit, 10...
・Dongfeng circuit, 11...K1 discrimination circuit, 12...1
．． 71 Moss Suitsuji, 13 (16)...ROM, 14.
...Register, 15...Summing circuit, 17...Multiplication circuit, d...Triangular wave data for address, (Z (0")
)-iT string wave generation data. Figure 7 Figure 8 Figure 10

Claims (1)

[Scope of Claims] Time axis data generation means for digitally creating a sawtooth wave, converting the sawtooth wave data into time axis data corresponding to a predetermined period of the sine wave, and outputting the time axis data; circuit means for obtaining data obtained by truncating predetermined bits of the data; and data from the circuit means is input as address data, and recorded data corresponding to the address data is in the form of a mathematical operation of sine wave data and the address data. A sine wave, comprising: a read-only memory that is the data of the read-only memory; and an output calculation means that performs an inverse operation of the mathematical operation using the time-axis data on the output of the read-only memory to obtain a sine wave. generation circuit.