JPH01278104A - Digital oscillator - Google Patents

Abstract

PURPOSE:To produce a sine wave with a slight amount of memory capacity by using an initializing circuit and continuing the oscillation while substituting properly the initial value to a secondary IIR digital filter. CONSTITUTION:The title oscillator consists of secondary digital filter IIR digital filter A composing of unit delay elements 1 and 2, a multiplier 11 and an adder 7 and an initializing circuit B substituting the initial value to both elements 1 and 2. When a sine wave is produced, a recurrence formula of a trigonometrical function is used as shown in an equation I. That is, sin(0), sin(x) sin(2x)... can be successively obtained with application of the initial values, i.e., sin(-x) and sin(-2x). Thus the sine waves are oscillated. As a result, a slight amount of the data memory capacity suffices owing to application of an oscillation theory where a single frequency is produced by arithmetic.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a digital oscillator, and more particularly to a sine wave oscillator using digital signal processing.

(Prior Art) Conventionally, digital oscillators using the following oscillation method are known.

Figure 3 shows the first oscillation method [Nippon Telegraph and Telephone Public Corporation “D7
It is an explanatory diagram of the 0-type automatic converter [11 Hardware (1), Telecommunications Mutual Aid Association, pp. 303-306].

In this figure, 1 is a sine wave, and 2 is a ROM that stores sine wave data. (a).

Figures (b) and (C) each show one period of l/
This indicates that sine wave data for 2 cycles and 174 cycles is stored. In this oscillation method, this sine wave data is created in advance in ROM2, and the RO
A sine wave is oscillated by reading the M data. Specifically, when using ROM data for one cycle, this is read out repeatedly for one cycle, and the ROM data for 172 cycles is read out repeatedly.
When data is used, it is read back as shown by the arrow in the figure (b), and when 1/4 cycle worth of ROM data is used, it is read out as shown by the arrow in the figure (C). A sine wave is created and oscillated by reading back and reversing the polarity in the second half of the cycle.

In addition, the second oscillation method uses data for one cycle (number of samples N) of a sine wave of one reference frequency fs to generate the following first oscillation method.
This method stores data in ROM as shown in the table and oscillates at an arbitrary frequency f according to this data and the calculations shown below [Texas Instruments Catalog, Digital Signal Processing Applications with the・T.M. Niss 320 Family (Digital Signal Process
ng Applications with
he 7MS3211) Family No. 269-27
Page 5) 1゜Table 1 The following describes how to oscillate a sine wave with a frequency based on this data. The ROM address of the sine wave with frequency f is determined according to the following equation (1).

mad (k-DELTA, N)
(1) Here, k and DELTA represent the following.

k=0.1.2.3. ...DELTA=f/fs
(2) Also, the operator "mad" is mod (a, b) = INT (a - [a/blxb)
(3) However, in formula (3), [X]
indicates the Gaussian symbol and represents the largest integer less than or equal to X.

Further, INT (X) is an integer of X, and one of rounding down, rounding up, and rounding is selected and set. The ROM address is calculated by sequentially changing the value of k to 0, 1, 2°3, . . . according to the above equation (1). By sequentially reading out the ROM data corresponding to this ROM address, a sine wave of frequency f can be oscillated. Incidentally, one cycle oscillates every time k is an integer multiple of N.

(Problem to be Solved by the Invention) However, the above oscillation method requires that sine wave data at the oscillation frequency or reference frequency be created in advance and stored in the ROM, and a sine wave with less distortion can be obtained. In order to achieve this, it is necessary to reduce the sampling period to a certain extent, so as the oscillation frequency decreases, the number of ROM data must be increased, which requires a large amount of data memory capacity. There were naturally limitations on its use for the purpose of obtaining it easily.

The present invention is based on a principle different from conventional oscillation methods, and it is not necessary to store data for 1 cycle, 172 cycles, or 1x4 cycles in ROM in advance, and oscillates a sine wave with a small memory capacity. The purpose of this invention is to provide a digital oscillator that can perform

(Means for Solving the Problems) The present invention provides two unit delay elements (1), (2), 1
A secondary I consisting of two multipliers (11) and an adder (7)
A digital oscillator comprising an IR digital filter (A) and an initial value setting circuit (B) for assigning initial values to each of the unit delay elements (1) and (2). .

(Function) Next, the oscillation principle in the digital oscillator of the present invention will be explained together with the function of the second-order IIR filter according to the present invention.

In the present invention, in order to generate a sine wave, a trigonometric recurrence equation shown by the following equation (4) is used.

5in(nx)=2◆cos(x)sin(n-1)x
-sin(n-2)x (4) In equation (4), by giving 5in(-x) and 5in(-2x) as initial values, sin(0), sin(
x).

sin (2x),... can be filled sequentially,
It can oscillate a sine wave. Note that the initial value is si
n(-x).

3in (-2x), and the two adjacent points sin(mx), sin((m-
1) x) (m is any integer). By appropriately changing the initial value, a sine wave (or cosine wave) with an arbitrary phase can be generated.

Next, the following analysis will be performed in order to provide means for realizing the above equation (4).

Now, y (n) = s in (nx)
(5). Substitute equation (5) into equation (4).

y (n) □2-cos (x) ・y (n-1)
-y (n-2) (6) For convenience, if we add x (n) = 0 to the right side of equation (6), we get y(n) = 2・cos(x)・y(n-1 )-y(n-
2)+x(n) (7). When formula (7) is Z-transformed, Y (z) = -111111cho1 and -X (z)
(8) 1-2・cos(x)・z '+z''. From equation (8), we can see that the coefficient of X (z), that is, the transfer function of the digital filter, has a second-order IIR filter type. In addition, the poles are expressed by equation (8)% and equation (9), and exist on the unit circle (see Figure 2).

Accordingly, the second-order IIR digital filter according to the present invention generates a sine wave according to the above equation (4) by providing two initial values a and b.

(Example) Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a drawing showing an example of an oscillation circuit used in the digital oscillator of the present invention. In this figure, A is 2
The next IIR digital filter, B is an initial value setting circuit. As the initial value setting circuit B, for example, initial values a, b
ROM storing these and a secondary IIR digital
It consists of a readout circuit for reading in synchronization with a basic clock for driving filter A. The initial value can be set in the same way as in a normal digital filter. In addition, 1.2 is a unit delay element, 3
is a multiplier, 4 is an adder, and 5 is an output terminal.

Next, the operation of the oscillation circuit shown in FIG. 1 will be explained using an example in which the period Ts of the oscillating sine wave is an integral multiple of the sampling period T (set by the delay time of the unit delay element).

The initial value setting circuit B gives initial values a=sin(mx) and b=sin((m-1)x) to the unit delay element 1.2, respectively.

The multiplier 3 calculates 2CO3(X)・sin(mx), and the adder 4 calculates this and the output s of the unit delay element 2.
If we add in ((m-1) x) with the opposite polarity, we get s
in(m+1)x is obtained and output from the output terminal 5.

Further, this output is input to the unit delay element 1, sin (mx) is input to the unit delay element 2, and sin (m+2)x is obtained by equation (4), which is output from the output terminal 5. Thereafter, in the same way, s in (m+3)
x.

sin (m+4) x, . . . , and a sine wave with a period Ts is output from the output terminal 5. Note that here, X represents 2πT/T (the same applies below).

By the way, in equation (4), as mentioned above, 2
There are two poles. The instability of the oscillation circuit caused by this can be eliminated by substituting the initial values a and b into the unit delay elements 1 and 2 every cycle of the oscillation sine wave.

Next, as another embodiment of the present invention, an oscillation method when TS/T is not an integer will be described.

When Ts/T is not an integer, that is, the following equation (10)
When the % formula is % (10) (here, the greatest common divisor of d and m is h), to generate a sine wave using the second-order IIR digital filter A in Fig. 1, for example, 1 is applied to QT. It is sufficient to substitute the initial values a and b into the unit delay elements 1.2 at a rate of
As becomes shorter, the S/N ratio of the output oscillation sine wave deteriorates. This is because the operation word length of the second-order IIR digital filter shown in FIG. 1 is finite, and the poles of the filter exist on the unit circle. In order to prevent this deterioration of the S/N ratio, it is necessary to
．． By assigning an initial value to 2, a method of shortening the word length can be adopted.

Next, a method of assigning one set of initial values to pT (p represents a natural number less than or equal to β) at a rate of one time will be described. Here, one set of initial values is a(4pT).

Let b((ξp-1)T). However, here 0 is a.

Show that b is a function of ξpT. Further, ξ represents a natural number from 1 to [12/p]-1 ([Xl represents a Gaussian symbol; the same applies hereinafter).

By the way, let ξ be 1, 2. ...The initial values a and b when closing are points on the oscillating sine wave set every 9 cycles, so a(ξpT) and b((! p-1)T)(
l・1,2. . . , each initial value of l≦[Q/p]−1) is also a point on another sine wave having a period different from that of the oscillating sine wave.

That is, we now conveniently assume that the output oscillation signal is a cosine wave, and θ7=2πT/T, (11
)θ8=2π−pθT (12
), the initial values to be substituted at time pT(!・1) are a=cos(-〇,), b=cos(-(θ8+θT
)) Also, the initial values to be substituted at time 2pT (ξ・2) are a=cos (-20s), b=cos(-(2θ8+
θT)). That is, the initial value a is cos (−ξ
θ,).

b is given as a point on cos(-(ξθ3+θa)). Then, cos(-ξθS) can be oscillated according to the following recurrence formula (13), as in the first embodiment. The two initial values a' and b' necessary for oscillation are, for example, a' = cos (0)
.

b'=cos(OS) can be used.

In addition, cos (-(ξθ6+θd)) is expressed by the following formula (14
), there is a relationship between the % expression %(). Therefore, by combining the above cos (ξθS) and the 5 inch (nθ3) oscillator, T, /
It can be seen that oscillation is possible even when T is not an integer.

Note that the two initial values a″ and b″ of 5in (nθS) are, for example, a″=sin (0), b″□5in
(θ3) can be used.

In short, in order to oscillate a cosine wave whose period Ts is not an integral multiple of the sampling period T using the second-order IIR digital filter shown in FIG. =cos(θT),
Assign b=cos (2θT), at time p'r, a=cos (θ,), b=cos (θ8+θT), and at time 2pT, a=cos (2θs)
, b = cos (2θ3 + θT), and the following initial values are substituted in the same way, and at time QT, a = cos
(θ7), b=cos (2θT), and at time ΩT+pT, a=cos (θ3), b=cos
(θ8+θT) and at time ΩT+2pT, a=cos (2θS)+b=cos (2θ8+θT
) and so on. As a specific example, Q
=20. The output waveform and the initial value to be set when m=3.20T:3T, p=6 are shown in FIG.

- FIG. 5 is a diagram showing an example of an oscillation circuit used in the digital oscillator of the present invention constructed based on the above analysis, and particularly shows an example of the construction of an initial value generation circuit. In this figure, A is a second-order IIR digital filter, and B is an initial value setting circuit. The initial value setting circuit B includes the second. 3rd 2
It is equipped with an order IIR digital filter. Also, 1
．． 2゜3.4, 5.6 are unit delay elements, 7, 8, 9゜1
0 is an adder, 11, 12, 13, 14.15 is a multiplier,
16, 17. 18, 19, 20. 21 are switches, 22
, 23, 24, 25, 26°27.28 all indicate terminals.

First, connect the switches 16 and 17 to the terminals 22 and 25, respectively, and connect the unit delay element 1.2 to the ROM (not shown).
After substituting the initial value a=cosθ7゜b=cos2θa stored in , switch 16.17 is connected to empty terminal 24.2.
Connect it to 7. At this time, in the oscillation circuit A,
In the same manner as in the first embodiment, the oscillation circuit A performs calculations once every sampling period T until the time reaches 9 o'clock, and outputs the results to the output terminal 28.

On the other hand, the initial value setting circuit B sets the initial value a at time pT.
', b' and a'', b'' are calculated.

That is, by closing the switches 18, 19, 20, and 21, the initial values cos (○) and cos (
0g), sin (0), -5in (OS)
Substitute and open switches 18, 19, 20, and 21. As a result, cos(lθ3) oscillates in the oscillation circuit C, and 5in(ξθ,) oscillates in the oscillation circuit. Then, based on this oscillation output, the multiplier 12 generates cos(lθS)・c
os (θT) and multiplier 13 to 5in (!θs)
15in(θT) is calculated, and the latter is inverted and added in an adder 8 to calculate cos(ξθ8+07). Then, at time pT, the calculation result is output to the terminal 23.26, and then the switch 16.17 is connected to the terminal 23.26, respectively.
Connect to. In this way, the initial value a=cos (θs
) , , b=cos (θ3+θT) are respectively assigned to the unit delay element 1°2, and then the switches 16 and 17 are connected to the empty terminals 24 and 27, respectively.

Then, the operation of the oscillation circuit A is performed again until time 2pT, and the result is output to the terminal 28. At time 2pT, the initial value setting circuit B performs the calculation again and the oscillation circuit A
The initial value a=cos (2θ
s), 1)=cos (2θ, +θT) is substituted. Thereafter, the above process is repeated until time QT=mTs. When time QT=mT3, unit delay element 1,
Initial value a=cos (θT) again at 2, 3, 4, 5.6
, b=cos (2θT) and perform the above processing. In this way, a cosine wave is generated. Note that the switches 16 to 21 in this embodiment are 2? Switching is performed in synchronization with the basic clock for driving the JIIR digital filters A, C, and D according to a conventional method.

Although the cosine wave has been explained here as an example, it goes without saying that a single frequency wave of any phase can be generated depending on how the initial value is given.

Furthermore, it goes without saying that a circuit similar to the above embodiment can also be implemented within a processor.

(Effects of the Invention) As described above in detail, according to the present invention, the secondary II
An R digital filter and an initial value setting circuit for assigning an initial value to the R digital filter are provided, and oscillation is maintained while appropriately assigning the initial value to the secondary IIR digital filter, so that the S/N ratio of the oscillation signal is Since it is based on the oscillation principle of creating a single frequency wave by calculation, the data memory capacity may be very small.

[Brief explanation of the drawing]

FIG. 1 is an oscillation circuit diagram of the first embodiment of the present invention, FIG. 2 is a diagram showing the poles of the transfer function in equation (8), and FIG. 3 is an explanatory diagram of the conventional first oscillation method. FIG. 4 is a diagram showing an output waveform and an initial value to be set when TS/T is not an integer, and FIG. 5 is an oscillation circuit diagram of a second embodiment of the present invention. A, C, D...Second-order IIR digital filter, B
...Initial value setting circuit. Patent applicant: Oki Electric Industry Co., Ltd., invented the first dormitory.

Claims (1)

[Claims] Two unit delay elements (1), (2), one multiplier (1
1) and an adder (7); and an initial value setting circuit (B) for assigning initial values to each of the unit delay elements (1) and (2). A digital oscillator comprising: