JPS5932039A - Generator of trigonometric function - Google Patents

Abstract

PURPOSE:To obtain simply a trigonometric function value, by generating the tigonometric function value corresponding to an input digital signal in the form of a digital signal by a storage element of a comparatively small capacity and with accuracy approximately equal to that of a conventional process. CONSTITUTION:A parallel digital signal (x) is decomposed by a word decomposer 1 into high-order and low-order word signals (a) and (b). The word (a) is branched to two parts and supplied to a signal switch 3 and a phase converter 2, respectively. The converter 2 performs an operation of an output signal (c) as c=pi/2-a. The switch 3 uses its output (d) to deliver the signal (a) for a period from a time point t1 through t2 and then the signal (c) at and after the time point t2. A storage element 4 delivers the cosine function value e(cosa) to the signal (a) and the sine function value e(sina) to the signal (c) respectively. A multiplier 6 obtains a product (g) of a signal f(cosa) and the signal (b), and an adder 7 adds this product (g) with the signal (e). Thus it is possible to obtain an output signal y=sinx at and after the time point t2.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention generates trigonometric function values in the form of digital signals corresponding to input digital signals. This invention relates to an electrical trigonometric function generator with high precision and small storage capacity.

In general, all periodic signals are decomposed into trigonometric functions using a Fourier series, and in dynamic linear system simulators and the like, a trigonometric function generator becomes an indispensable component when inputting disturbances and the like.

Conventionally, in order to generate a trigonometric function value as a fully digital value, a storage element is used in which the trigonometric function value corresponding to the angle is calculated in advance and stored at an address corresponding to the input angle signal, and the input signal is stored at that address. A common method was to apply a trigonometric function value corresponding to the input signal as an output signal by reading the contents.

Therefore, since there is a one-to-one correspondence between the input signal and the address within the storage element, there is a drawback that an enormous storage element capacity t is required in order to obtain all highly accurate trigonometric function values.

The present invention overcomes the above-mentioned drawbacks and provides a complete trigonometric function generator with as much accuracy as conventional methods, but with a relatively small capacity storage element.

The trigonometric function generator according to the present invention includes a word decomposer that decomposes an input angle signal, which is a parallel digital signal, into an upper word and a lower word at appropriate pit positions, a phase converter that completely changes the phase of the upper word, and a phase converter that completely changes the phase of the upper word. A signal switch for switching between the output of the converter and the upper word of the word resolution output, a storage element that generates a trigonometric function value corresponding to the output of this switch, and a delay that stores this trigonometric function value for a certain period of time. It consists of a circuit, an adder that calculates the bond between the output of this delay circuit and the lower word of the word decomposition amount output, and a timing circuit that controls the flow sound of the signal.

Next, embodiments of the present invention will be described with reference to the drawings.

First, an embodiment of the present invention will be described with reference to FIG. 1 and FIG. 2. Note that in FIG. 2, time delays of adders/subtractors and multipliers are not shown for ease of understanding.

This example is an example of a function generator that generates all sine function values. That is, it is assumed that the function generator is given an input digital angle signal X and outputs y such that y=sinx as a digital signal.

In FIG. 1, the parallel digital signal X is input to the word decomposer 1 at time t1 in FIG.
is decomposed into an upper word signal a and a lower word signal 6 at a fixed pit position.

Specifically, this word decomposer 1 can be easily realized by simply decomposing all the parallel signal lines of the input signal X into upper and lower sides. Upper word signal a output from word decomposer 1
is branched into two, one of which is input to the signal switch 3,
The other is input to the phase converter 2.

The phase converter 2 performs an operation such that its output signal C becomes C=π/2-a (Asian). This phase converter can be easily realized by simply reversing the high and low logic levels by setting the input signal to be 0 to π/2 (Asian) in advance.

The signal switching device 3 is controlled by the control signal shown in FIG. 2 so as to output the signal a as its output d from time 1° to time t2, and output the signal cTh after time t2.

Thus, the upper word a of the input angle signal is applied as an address to the storage element 4 in which the cosine function value corresponding to the address value is stored in advance for 1 cd between time t1 and time t2, and the cosine function value e corresponding to a is applied. (cos
a) is output and input to the delay circuit 5.

On the other hand, the signal switcher output d after time t is the phase converter output C, as described above, and is applied as the address of the memory element 4. Therefore, time t! The subsequent output e of the memory element 4 is e=cosd=cosc=cos(x/2-a)=si
When na and shi, the sine function value (sina) is obtained.

Also, time 1. Thereafter, the cosine function value f (cosa) output from the delay circuit 5 is input to the multiplier 6 along with the lower word signal of the word decomposition amount output, and the multiplier 6 calculates the signal f and the signal fR. do.

This product signal g is connected as an input to an adder 4 whose one input signal is e, is summed, and becomes an output/output device y after time t2.

It is clear from the discussion below that this output signal y is a sine function value of the input signal X.

In general, if we perform Tiller expansion as the function value f (x) t y of X, then y = f (f for x (xt + Rewritten to correspond to y=sinx Furthermore, taking into account everything in Figure 2, between time t1 and time t2 C2π/2-a d=a After time t2 C-π/2-a d=c e=COS C=S 1 n a f=cosa g=f11b-CO5a11b y=e+g=sina+cosaeb
Equation (2) and Nada 2) match equation (1).

Note that, taking into account the time delay of the adder/subtractor and the multiplier, the output y may be sampled after time t3 in FIG. 2.

Also, if the output d of the signal switch 3 becomes the signal C between time 11 and time t8, and becomes the signal a after time t2, the calculation at the adder 7 becomes y=e−g. , the output y is y=e−g=cosa−sina−b in cos(x), and can be easily converted to a cosine function generator.

As explained above, according to the present invention, trigonometric function values can be easily determined by linear interpolation by utilizing the fact that the differential of a sine function is a cosine function, and the differential of a cosine function is a sine function. Therefore, in a trigonometric function generator using a read-only storage element consonant, it is possible to manufacture a trigonometric function generator with a small storage element capacity and high accuracy.

[Brief explanation of drawings]

FIG. 1 is a schematic diagram showing an embodiment of the present invention. FIG. 2 is a basic timing chart of each signal shown in FIG. 1... Word decomposer, 2... Phase converter, 3... Signal switch, 4... Memory element, 5... Delay circuit, 6...multiplier,
7... Adder, 8... Timing circuit.

Claims (1)

[Claims] A word decomposer that decomposes an input angle given by a parallel digital signal into an upper word and a lower word at appropriate bit positions, a phase converter that changes the phase of the upper word, and a phase converter that converts the output of this phase converter and the upper word. A signal switch that outputs a cutting blade, a storage element that generates a trigonometric function value corresponding to the output of this signal switch, a delay circuit that stores all the trigonometric function values generated from this storage element for a certain period of time, and this delay. a multiplier that calculates the product of the circuit output and the lower word of the output of the word decomposer; an adder that calculates the sum of the multiplier output and the trigonometric function value from the storage element; and a signal between each of the components. A parallel digital trigonometric function generator whose basic principle is -order interpolation processing.