JPH02272807A - Waveform generation device - Google Patents

Abstract

PURPOSE:To obtain a target random number with satisfactory reproducibility by installing a conversion program which converts random number initial value group data into the uniform random number data row of an M sequence and a conversion program which converts the data row into the random number data row of a target distribution form. CONSTITUTION:Random number initial value group data which is read from a first memory 1 is converted into the uniform random number data row of the M sequence in accordance with the conversion program stored in a second memory 2, and the uniform random number data row of the M sequence is converted into the random number data row of the target distribution form (normal distribution, for example) in accordance with the conversion program stored in a third memory 3. Then, the converted random number data row of the target distribution form is stored in a waveform memory 4 as waveform data, and stored waveform data is read in a D/A converter 5 and converted into an analogue signal. Thus, the target random number including a normal random number can be generated with satisfactory reproducibility.

Description

DETAILED DESCRIPTION OF THE INVENTION <Industrial Application Field> The present invention relates to a waveform generation device, and more particularly, to an improvement in a device that digitally generates pseudo white noise.

<Prior art> Random numbers used in noise simulation are −-like random numbers, normal random numbers, exponential random numbers, or
It can be classified into binomial distributed random numbers, Poisson distributed random numbers, etc.

Here, −-like random numbers are used to determine the sample number for random sampling, extract test data from a specific file, etc., normal random numbers are used to generate circuit thermal noise and demand quantity for inventory simulation, etc., and exponential random numbers are used to generate demand for circuit thermal noise and inventory simulation. is used for queuing simulation, binomial distributed random numbers are used for quality control, and Poisson distributed random numbers are also used for queuing simulation.

By the way, as a device that digitally generates such noise, a predetermined interval [-1
, 1] that generate uniform random numbers, and those that generate uniform random numbers by specifying a noise function are used.

<Problems to be Solved by the Invention> However, the uniform random numbers output from these devices are noise that does not exist in reality, and are not preferable as output signals of waveform generators that simulate real waveforms.

In addition, the present invention focuses on this point that it is desirable to use normal random numbers when simulating noise in various electric circuits, and the purpose is to generate desired random numbers including normal random numbers with good reproducibility. An object of the present invention is to provide a waveform generator that can generate a waveform.

Means for Solving the Problems> The waveform generator of the present invention includes a first memory for storing random number initial value group data, and a random number initial value group data read from the first memory in an M series. a second memory that stores a conversion program for converting into a uniform random number data string; and a second memory that stores a conversion program for converting the M-series uniform random number data string converted according to the conversion program stored in the second memory into random number data in a desired distribution form. a third memory that stores a conversion program for converting the data into a column; a waveform memory that stores, as waveform data, a random number data column of a desired distribution format converted according to the conversion program stored in the third memory; A D/A converter converts waveform data read from the memory into an analog signal.

Effect> In the present invention, random number initial value group data read from the first memory is converted into an M-series uniform random number data string according to a conversion program stored in the second memory,
This M-series uniform random number data string is converted into a random number data string with a desired distribution form B (e.g. normal distribution) according to the conversion program stored in the third memory, and this random number data string with the desired distribution form is It is applied as waveform data to a D/A converter and converted into an analog noise signal.

<Example> Hereinafter, embodiments of the present invention will be explained in detail with reference to the drawings.

FIG. 1 is a block diagram of essential parts of an embodiment of the present invention. The first memory 1 stores random number initial value group data. The second memory 2 stores a conversion program that converts the random number initial value group data read from the first memory 1 into an M-series uniform random number data string. 3rd memory 3
A conversion program for converting an M-sequence uniform random number data string converted according to the conversion program stored in the second memory 2 into a random number data string having a desired distribution form (for example, normal distribution) is stored. The random number data string in a desired distribution form converted according to the conversion program stored in the third memory 3 is stored in the waveform memory 4 as waveform data. The waveform data stored in the waveform memory 4 is read out to the D/A converter 5 and converted into an analog signal. Each of these memories 1 to 4 is connected to a calculation control unit (CPtJ) 7 via a bus 6. In addition, on bus 6,
Other memory, keyboard, display, etc. are also connected, but are not shown.

The operation of the device configured in this way will be explained.

When random number generation is specified, the random number initial value group data (Ut
) (t=t~31) is read out and transferred and stored in a RAM area (not shown). Further, a □ pointer indicating the starting position of the random number work area is also stored in the RAM area (step (2)).

By having initial value data in the table like this,
It is possible to give reproducibility to the generated noise.

Thereafter, an M-sequence uniform random number data string is generated using the random number initial value group data transferred and stored in the RAM area, and a normal random number data string is further generated using this −-like random number data string.

The M-series uniform random numbers are white noise with excellent reproducibility that can be easily generated using a combination of a shift register and an exclusive OR gate.

For example, assuming that the constants C4, C2,...+CP-1 are all 0 or 1 and cp=1, the recurrence formula ai =C
+ aL-+ -)-c2 ai-2+°”+ c p
a t −p (iod2) −(1)
(nod2 is the remainder system of 2) A binary signal consisting of 0 and 1 (ai
)think of. Initial value a O+ ”” + a P −1
is such a series (aL
) has a maximum period of m = 2'-1, and this sequence (ar) is called an M sequence, where ai is the maximum period m
The condition for having is f(x) = 1 + Cl Z + + c p x'
- The polynomial represented by (2) becomes a primitive polynomial.

The fact that f(x) is a primitive polynomial means that f(x) cannot divide the polynomial χ-1 when ■O<k, 2-1, and only when k = 2'-1. This means that the conditions are met.

Since the M sequence is a binary signal consisting of 0.1, (aLl
Let us consider that two numbers (e≦p) are taken out and lined up to create an e-bit binary decimal number (Uk), and this is used as a uniform random number on the interval (0°1).

First, the following trinomial is selected as the aforementioned primitive polynomial.

f(X)=Z'+χ$+1
, -, (3) Therefore, (+), from equation (2), (a 盈) is aL=a7-P +ai-'i (
iod2) =・(4).

At this time, a binary decimal number (Ukl) is defined as follows.

Uv=O, at at +r...ai p-1r
-(5) (r is an integer that is 2≦p and is coprime to the period m) The calculation of equation (4) above is an addition that ignores carry and is the same as an exclusive OR, and can be performed at high speed. Can calculate. Therefore, fUi) can be generated by Uk=tJk-peUk-1 (6). Note that ■ is a bit-wise exclusive OR.

Specifically, the numerical value is divided into 32 bits with 16 bits each for the integer part and the decimal part.
Treated as a bit fixed point type, this determines the number of bits of tJk, 2=16. Furthermore, although various primitive polynomials are known for equation (3), the set of p and q that requires a small number of initial values is selected, and p=31. p-q=6...(
7).

As a result, the period m of the M sequence is m=2"-1ki2.lXl0" (8)
become.

As is clear from equation (1), such a method requires p fixed-point initial values. Therefore, we use the mixed congruence method as a simple way to generate uniform random numbers.
Uniform random numbers are generated on (0, 2''-1), and p of them are adopted as initial values.

By the way, it is inconvenient to use only uniform random numbers as random numbers.
In particular, normal random numbers are required for circuit noise simulation.

Such normal random numbers can be obtained by applying the central limit theorem using −-like random numbers in the interval (0, 1).

Since the −-like random number in the interval (0,1) follows a uniform distribution, its probability density variable p(X) becomes, therefore, the average μ is μ = f no χ? PC7-n b = Σ
...0Φ
and the variance σ2 is d' = /, 'Z''F('x-)*%-Z'
72 = (11).

When n -like random number sequences (Utl) in the interval (0, 1) are averaged, the average value χi is given by the central limit theorem when n is sufficiently large. Average μπ = 1/2 Variance σ2 = 1/( 12n).Therefore, r in the following equation is a random number λ with mean 01 variance σ), which is obtained from the random number r of normal distribution N(0, 1) by the following equation.

λ=μ+σr...(13)
FIG. 3 is a flowchart showing the flow of such processing.

First, in step (1), the pointer stored in the random number work area is read out. Next, the total K (ar) stored in another work area is initialized to 0 (step (2)), and then to determine whether the number of loops has reached 12 (step (3)). If the number of loops has not reached 12, select Uk-P from the random number work area while moving the pointer. (Step (4)), then read Uk-pus (Step (5)), calculate the exclusive OR of these tJk-P and Uk -1) +4 (Step (6)), and the result is Uk.
is stored in the random number work area (step (7)), then it is determined whether the pointer is at the bottom of the random number work area (step (8)), and if it is, the pointer is moved to the beginning of the random number work area. (step (9)), and in a state where the pointer is not at the bottom of the random number work area, Uk is added to the calculated value r (step 0Φ), and the process returns to step (3) for determining the number of loops. On the other hand, when the number of loops reaches 12, subtract 6 from the calculated value r to remove the average value (Stelaph Responsibility 11)), and calculate (reduce Mr by 1/4).
Multiply the current position of the pointer (step (12)), then store the current position of the pointer in the random number work area (step (13)
)).

FIG. 5 is an explanatory diagram of the uniform random number Uk obtained by executing such a procedure, and (a) is an illustration when the number of data k is 3.
(b) shows the histogram of (a), and (C) shows the autocorrelation function Rχχ(1) up to lag 200 for the data string of (a). It can be seen that at lag t~0, the autocorrelation function Rχχ(1) has a small value, indicating that whiteness is destroyed. Such excellent whiteness of −-like random numbers is important when generating random numbers of other distributions.

FIG. 6 is an explanatory diagram of the normal random number λ obtained by executing such a procedure, and (a) is an illustration when the number of data k is 3.
(b) shows a histogram of <a), and (C) shows the autocorrelation number Rxχ(1) up to lag 200 for the data sequence of (a). As is clear from this (c), excellent whiteness is maintained even with the normal random number λk.

FIG. 7 is a noise spectrum diagram obtained by the configuration of FIG. 1. Here, the clock rate of data output is 1
00HH2, and the data period is set to 81.92 μs.

With this configuration, the initial values are tabled and fixed, making it possible to reproduce noise. This is an essential requirement for a waveform simulator.

Furthermore, the period until the noise repeats the same value can be made sufficiently long, and by discarding the initial part, it can be treated as substantially different noise data.

Further, the basic uniform random number can be generated by one exclusive OR, and the data calculation time can be shortened.

Furthermore, since the distribution and standard deviation of the noise output in this manner are known, the user can easily change the noise to have desired characteristics, and even set the S/N ratio.

In addition, in the above description, an example was explained in which −-like random numbers are converted to normal random numbers, but it may be converted to other random numbers depending on the purpose.

<Effects of the Invention> As described above, according to the present invention, a waveform generation device capable of generating desired random numbers including normal random numbers with good reproducibility can be realized, and is suitable as various noise signal devices.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIGS. 2 and 3 are flowcharts showing the operation procedure of FIG. 1, FIG. 4 is a diagram explaining the characteristics of uniform random numbers, and FIG. FIG. 6, which is an explanatory diagram of the characteristics of normal random numbers, is a spectrum diagram of a noise signal output from the apparatus of FIG. 1. 1... first memory (random number initial value group data), 2...
・Second memory (M-series-like random number data string conversion program), 3...Third memory (desired distribution form random number data string conversion program), 4...Waveform memory, 5...D
/A converter, 6... Bus, 7... Arithmetic control unit (CP
U). Diagram

Claims (1)

[Claims] A first memory that stores random number initial value group data, and a conversion program that converts the random number initial value group data read from the first memory into an M-series uniform random number data string. a third memory that stores a conversion program that converts the M-series uniform random number data string converted according to the conversion program stored in the second memory into a random number data string of a desired distribution form; a waveform memory that stores, as waveform data, a random number data string of a desired distribution format converted according to the conversion program stored in the third memory, and converts the waveform data read from the waveform memory into an analog signal. A waveform generator comprising: a D/A converter; and a D/A converter.