JPS6313506A - Sinusoidal wave generating method - Google Patents

Abstract

PURPOSE:To obtain a sinusoidal wave with an excellent weveform by setting a step width decided by a frequency of a sinusoidal wave and using a multiplier, an adder or a subtractor so as to calculate the next sample of the sinusoidal wave sequentially thereby decreasing the memory capacity. CONSTITUTION:A multiplier MUL and an adder(subtractor) ALU are provided and four memories are used for the sequential calculation. That is. when four values {sin(n-1), cos(n-1)} and steps {sind(1), cos(1)} are given in the memories. {sin(n), cos(n)} are calculated by using the multiplier and the adder (subtractor) to calculate recurrence formulae sin(n)=sin(n-1)cos(1)+cos(n-1)sind(1), and cos(n):cos(n-1)cos(1)-sin(n-1)sin(1). A wave approaching infinitely an ideal sinusoidal wave theoretically is generated by continuing the calculation above.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a modulator (demodulator) that uses a sine wave table in digital signal processing.

(Prior Art) Conventionally, in digital signal processing, when a sine wave of a certain frequency is required, values (sample values) at all sample points of a sine function or a cosine function are used.

FIGS. 3(u) and 3(b) show a table of a sample string of a conventional sine function and a memory sample value. The initial value is (0).

Similarly, FIGS. 4(a) and 4(b) show a table of sample strings of the Coa1 function and memory "2/1" combination values.

Next, the operation of the conventional example will be explained.

For example, when using the sine function, the address value of memory "2" (hereinafter referred to as MA) is initially set to 0, and each time processing at each sample interval is completed, 1 is added to MA, and the next The sample value of MA-1= is loaded in the process. The same applies to the cos function.

In this way, even in the conventional example described in Section 2, if all sample values of the sine function and CO8 function are stored in memory,
You can use the sine wave table as is.

(Problems to be Solved by the Invention) However, the conventional positive 11+2 wave generation method described in () requires a large memory capacity.

For example, for a table of one function, if the sampling frequency is fs and the frequency of the sine wave is F, then Ofs = mF (<1.m is the smallest natural number)
...A table of m samples that satisfies ■ is required.

For example, if fs=16KHz and F=4010Hz, a table of 1600 samples is required.

The same applies to the COS function.

As described above, the conventional method has the problem of requiring a large memory capacity.

The present invention solves these conventional problems and provides an excellent sine wave generation method that can reduce memory capacity.

(Means for Solving the Problems) In order to achieve the above object, the present invention provides a multiplier and an adder (subtractor) and performs sequential calculations using four memories, thereby generating a sine wave. It is designed to generate a table.

FIG. 1 is a block diagram of the sequential calculation method according to the present invention.
The sequential calculations using the memory, the multiplier, and the adder (subtractor) are shown below.

(Function) The present invention has the following function by virtue of the configuration shown in FIG.

In FIG. 1, when n = a + 1, here,
It is.

The starting point value of the table (sjn(lI), cos(a)
) and step size (sin(1), cos(])) are stored in memory.

Next sample value (sin(a+1), cos(a+1)
) is calculated using the following formula using a multiplier and an adder (subtractor).

5in(a + ]) = 5in(a)cos(1)
+cos(a)sin(1)−■cos(a+1)
=cos(a)cos(1)-sin(a)sjn(1
) − ■ Calculated here (sin (++ +1), eo
s(a+1)) are stored in memory.

Next, in the same way, (sin(]), co8(1)) and (
sin(a+1), cos(a + ])), then (
sjn(a+2), cos(a+2)) can be calculated.

-3 = In other words, if the four values of (sun (n-1), cos (n-1)) and step size (si, n (1), cos (1)) are in memory, multiplication Using a container, an addition (subtraction) machine,
By calculating the following recurrence formula, 5in(n) = sin(n-1)cos(1) +c
os(n-1) sin(1)...■ cos(n) =
cos(n-1)cos(1)-sin(n-1)si
n(1)...■(sin(n), cos(n)) can be calculated. By continuing this calculation, it is possible to theoretically generate an infinite number of sine waves.

(Example) FIG. 2 is a flowchart in an example of the present invention. The flow is similar to that in Figure 1, but the initial value a =
It is O.

Here, the operation shown in FIG. 2 will be explained.

To initially set the desired frequency of the sine wave, the step size (A, B) is stored in memory.

The values of (sin(0), cos(0)) at the starting point must be substituted.

As shown in the above action, (sun(n-1), cos(n
-1)) and (A, r'l) to (sin(n), cos
(n)) can be calculated.

When n matches the number of tables rn, go back and write (s
un(0), cos((1)) J: Start.

In this way, according to the above embodiment, normally, from the four values in memory and the initial values (sin(0), cos(0)), Calculate table values.

(Effects of the Invention) The present invention has the following effects as is clear from Example 1.

(1) Since table values are calculated sequentially using a multiplier and an addition (subtraction) board, the memory capacity can be extremely reduced.

(2) When changing the frequency of the sine wave, the step size (A, B
) can be easily done by changing the value of

(3) By changing the initial values (sf(,1), cos(II)), a positive limb wave can be generated from any phase.

[Brief explanation of the drawing]

Fig. 1 is a block diagram of the sequential calculation method in the present invention, Fig. 2 is a flowchart in an embodiment of the present invention, and Fig. 3 is a sample sequence of the sun function in the conventional example and a table of sample values in memory. FIG. 4 is a diagram showing a sample string of a cos function and a table of sample values in memory L in a conventional example. Patent applicant Matsushita Electric Industrial Co., Ltd. Figure 3 (o) (b) 4
figure

Claims (1)

[Claims] By providing a multiplier, an adder or subtractor, and a memory, initially setting the step size determined by the frequency of the sine wave, and substituting the initial value, the multiplier, adder, or subtraction is performed from these values. A sine wave generation method characterized in that the next sample value of a sine wave is calculated sequentially using a sine wave generator.