JPS5839328B2 - walshyukansuhatsuseiki - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a Walsh function generator.

The Wal sh function was written in J. by Mr. Walsh in 1922.
The function presented in 2017 is a complete orthonormal system with only two values, +1 and -1, and the WalshF using the Walsh function
Ourier series is a trigonometric function system.
It has properties very similar to series, and has been applied to waveform synthesis, waveform analysis, and a wide range of other fields using the Walsh function system.

Binary +1 in Walsh function. -1 is converted into a binary value of Oll in order to easily realize it as a digital circuit, the waveform f(t) can be expressed by the following equations (1) and (2).

However, Wi (t) is a Walsh function, Ci is a Walsh-Fourier coefficient, and can be determined by the following equation.

As shown in equations (1) and (2), < Wa of the Walshfm number system
lsh -Fourier series and trigonometric system Four
Although it has very similar properties to the iei number, the Walsh
Since the function Wi (t) consists of only 1,002 values, the L Wal sh function can be easily generated in a digital circuit.

2. Since the Walsh function is a discontinuous function, a linearly independent function can be easily created by shifting it horizontally using a shift register or the like.

3. A system using a digital method uses a device for waveform synthesis and waveform analysis using a trigonometric function system Fo.
Wal sh function system compared to urier series
It has the characteristic that it is more suitable to use the sh -F ourier series.

The applicant first proposed that W is an orthogonal function that can be expressed as 1.0.
We proposed a musical waveform generator using the alsh function (
(See Japanese Patent Application No. 109859/1983).

Attached Figures 1 and 2 are explanatory drawings of one embodiment of the above proposal, in which FIG. 1 is a circuit diagram of an embodiment of the Walsh function generator, and FIG. 2 is a circuit diagram of the Walsh function generator shown in FIG. 1. A time chart of the Walsh function of the function generator is shown.

The embodiment of FIG. 1 consists of a clock pulse generator, 1.4 1/2 frequency divider groups, 2.11
It is composed of circuit group 3, and generally the Walsh function generator up to the (2m-1)th order includes a clock pulse generator, m 1/2 frequency divider groups, and (2m-m-1) E of
It can be configured from a group of xclus 1ve-OR circuits.

The Walsh function generator shown in FIG. 1 receives clock pulses from a clock pulse generator 1, and a 1/2 frequency divider group 2 and an exclusive-OR circuit group 3 perform sequential circuit operations. There is.

As a result.

1. Wals at any time of the Walsh function
It is not possible to directly read the h function value.

2. When the time of the Walsh function is arbitrarily changed, W
The alsh function value cannot be read.

3. Multiple reading of the Walsh function generator is not possible.

It has disadvantages such as '.

The present invention has been made in view of this point, and is different from the previously proposed system that performs sequential circuit operation such as the Walsh function generator.
This provides a method for outputting the Walsh function value at that time by externally specifying a value (time code) representing the time of the Walsh function to the sh function generator.
The aim is to eliminate the aforementioned drawbacks in Walsh function generators.

Below, in the Walsh function generator, the order of the Walsh function is j, the time is R, and the Walsh function is W(j, k
), and the present invention will be described in detail with reference to the drawings.

FIG. 3 shows an embodiment of the invention.

In the figure, 10 is a memory circuit (read only, memo) that stores the Walsh function (j, k).
ry ), 11 indicates an address decoding circuit.

Assuming that the memory circuit 10 takes the order of the WalshM number in the vertical direction and the time in the horizontal direction, the Walsh function generator up to the (2m-1) order has a capacity (2m, 2m) of (2m, 2m).
It consists of a memory with 2m bits (x2m-22mbits).

For example, in the case of m=4, the memory is (16,1
6), Wal (0) ~Wa shown in Fig. 2
When storing the waveform shown in the time chart up to l(15) in the memory, the time code is, for example, m=
4, it can be encoded as follows. Therefore, by connecting the time code k to the address decoder 11, the memory 1
From 0, the value at the time of the Walsh function can be extracted.

FIG. 4 shows another embodiment of the invention.

The circuit configuration in the figure is such that the 1/2 frequency divider group 2 of the Walsh function generator shown in FIG.
1 address can be specified by time code,
The output of the memory circuit 21 is
- It is connected to the same circuit 22 as the OR circuit group 3.

The sequential output at each time of the 1/2 frequency divider group 2 shown in FIG. 1 is shown in the time chart of FIG.

(If m = 4). That is, WaI(1),
Wa 1 (3), Wa 1 (7) and Wa t (15
), the waveform shown in FIG. 5 can be easily understood by referring to the time chart of FIG.

In the Walsh function generator, the (2m-1)th
To store the functions up to the next one requires a memory capacity of (m, 2m), so as mentioned above, when m = 4, (
A memory circuit 21 having a memory capacity of 4, 16),
By applying the time code to the address decoder 20, a signal identical to the output signal of the 1/2 frequency divider group 2 in FIG. 1 is obtained from the memory 21, and the output is
If connected to the -OR open circuit group 2, a Walsh function specified by a time code can be generated at its output.

FIG. 6 shows a circuit configuration of another embodiment of the present invention.

In the same figure, 30 is a time code converter, 31 is an Exc
This is a lusive-OR circuit group.

As mentioned above, the time code can be encoded, so if an address is specified in the waveform of FIG. 2, the time code can be encoded as Wal (1), Wal (3), etc.
In order to correspond to Wal (γ) and Wal (15), not conversion is required.

Therefore, when m=4, the time code conversion circuit is
As shown in the figure.

The time code conversion circuit receives a time code from the outside and converts the time code using a logic circuit so that the output is the same as the output of the memory circuit 21 shown in FIG.

The output of the time code converter 30 is Exclusive-
It is connected to an OR circuit group 31 (same as 3 shown in FIG. 1), and can generate a Walsh function at a specified time as its output.

As described above, the Walsh function generator of the present invention does not generate sequential output, but generates a Walsh function that directly outputs the Walsh function corresponding to the time code by specifying the time code. Since it is a device that can easily perform digital control, calculation, and multiple readout, its application range is extremely wide and it will be industrially effective.

[Brief explanation of the drawing]

Figures 1 and 2 show the Wal
The circuit configuration and time chart of the sh function generator are shown. FIG. 3 shows an explanatory diagram of a circuit configuration of an embodiment of the present invention. FIG. 4 shows a circuit configuration of another embodiment of the present invention, and FIG.
The figure shows the output waveform of the 1/2 frequency divider group 2 shown in FIG. FIG. 6 shows a circuit configuration of still another embodiment of the present invention, and FIG. 7 shows an example of the circuit of the code converter 300 shown in FIG. In FIG. 4, 20 is an address decoder, 21 is a memory circuit, and 22 is an exclusive-OR circuit group.

Claims (1)

[Claims] 1. In a Walsh function generator,
By specifying a time code representing the time of the Walsh function from the outside, the Wal corresponding to that time code is
A Wal characterized by outputting an sh function value.
sh function generator. 2. The Walsh function generator according to claim 1, wherein the Walsh function generator comprises a memory circuit for storing the WalshJg value. 3 The Walsh function generator has a memory circuit and Exc
The Walsh function generator according to claim 1, comprising a lusive-OR circuit group. 4. The Walsh function generator according to claim 1, wherein the Walsh function generator includes a time code converter and an Exclusive-OR circuit group.