JP3358720B2 - Apparatus and method for generating noise waveform - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method for generating a noise waveform, and more particularly, to a method for generating a non-periodic noise waveform.

[0002]

2. Description of the Related Art Conventionally, a random number sequence is generally used to evaluate the effect of noise by simulation. However, a continuous system noise waveform must be generated for use in continuous system simulation such as circuit simulation. Is required. Further, generation of a noise waveform having desired characteristics such as 1 / f is required. In order to respond to this request, as shown in FIG. 8, a random number sequence having a normal distribution and a filter having desired characteristics are prepared, and a simulation of the filter is performed using the random number sequence as an input, so that a desired output from the filter is obtained. Generally, a noise waveform having the following characteristics is generated. Such a scheme is
For example, "IEEE Circuit &Device" issued in May 1996
s "pages 22-27. E. FIG. Thain and J.M. A. C
It is disclosed in a paper co-authored by onnelly. In this example, a noise waveform having a characteristic of H (f) is generated by passing through a filter having a transfer function H (f).

[0003]

However, in the above-mentioned conventional method, a filter having desired characteristics must be designed since the filter passes. However, designing a filter having desired characteristics requires expertise in filter theory and approximation theory, which is not easy for non-specialists. Furthermore, there is no guarantee that the approximation can be performed with sufficient accuracy depending on the characteristics.

An object of the present invention is to provide an apparatus and a method for generating an aperiodic noise waveform whose characteristics can be easily approximated.

[0005]

In order to achieve the above object, the present invention provides a frequency band corresponding to a desired frequency characteristic,
Using discrete wavelet transform, band dividing means for dividing into a plurality of non-overlapping bands, and the magnitude of noise in each band divided by the band dividing means are set so as to approximate desired frequency characteristics. Setting means, noise generating means for generating noise of a magnitude set by the setting means for each band, and synthesizing means for synthesizing the noise generated by the noise generating means, wherein the setting means A random number generating unit that generates a random number weighted for each band divided by the band dividing unit, wherein the noise generating unit sets a coefficient of a basis function in the discrete wavelet transform by the random number. It is characterized by having means for generating noise in each band.

Further, according to the present invention, a frequency band corresponding to a desired frequency characteristic is divided into a plurality of non-overlapping bands using a discrete wavelet transform, and each frequency band is approximated to a desired frequency characteristic. By generating a random number weighted for each band by setting the magnitude of noise in a band, and setting a coefficient of a basis function in the discrete wavelet transform by the random number, the magnitude set for each band In this case, the noise is generated, and the noise for each band is synthesized.

In the noise waveform generating apparatus according to the present invention, the band dividing means divides a frequency band corresponding to a desired frequency characteristic into a plurality of non-overlapping bands by using a discrete wavelet transform. Also,
The setting means sets the magnitude of noise in each band divided by the band dividing means so as to approximate a desired frequency characteristic, and generates a random number weighted for each band. Then, the noise generation means generates a noise of the magnitude set by the setting means for each band by setting the coefficient of the basis function in the discrete wavelet transform by a random number, and the synthesis means generates the noise by the noise generation means. The synthesized noise is synthesized. With such a configuration, a noise waveform having desired characteristics can be easily generated without using a filter theory or an approximation theory.

In the noise waveform generating method according to the present invention, a frequency band corresponding to a desired frequency characteristic is divided into a plurality of non-overlapping bands using discrete wavelet transform. The magnitude of noise in each band is set so as to approximate the frequency characteristics, and a random number weighted for each band is generated. Then, by setting the coefficients of the basis functions in the discrete wavelet transform by random numbers, a noise of a magnitude set for each band is generated, and the noise of each band is synthesized, so that the filter theory or the approximation theory is obtained. , A noise waveform having desired characteristics can be easily generated.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a noise waveform generating apparatus and method according to the present invention will be described below.
FIG. 1 is a block diagram showing a functional configuration of a noise waveform generation device according to an embodiment of the present invention. The noise waveform generating device includes a band dividing unit 10, a setting unit 20, a noise generating unit 30, and a combining unit 40. Then, the band dividing means 10 divides a frequency band corresponding to a desired frequency characteristic into a plurality of non-overlapping bands. The setting unit 20 sets the magnitude of noise in each band divided by the band dividing unit 10 so as to approximate a desired frequency characteristic.

The noise generating means 30 generates noise of the magnitude set by the setting means 20 for each band. Further, the synthesizing unit 40 synthesizes the noise generated by the noise generating unit 30. In the noise waveform generation method according to the present embodiment, the following three operations are performed. First, a plurality of divided bands are weighted so as to approximate desired frequency characteristics. Thereafter, the above-mentioned weighted random numbers are generated for each band, and a noise waveform having a frequency component of each band is generated. Next, the noise waveforms of the respective bands are combined to generate an overall noise waveform. Therefore, a noise waveform having desired characteristics can be easily generated without using a filter theory or an approximation theory.

Hereinafter, specific embodiments of the present invention will be described in detail with reference to the drawings. FIG. 2 is an explanatory diagram showing an approximation method of the frequency characteristic of the present example. In FIG. 2, the horizontal axis represents frequency, and the vertical axis represents gain. As shown in the figure, in this example, a frequency band corresponding to a frequency characteristic of a desired noise waveform is divided into non-overlapping frequency bands. Then, the size of each band is set so as to approximate the frequency characteristic of the desired noise waveform. Next, a discrete wavelet transform will be described with reference to FIGS. 3 and 4 as a method of dividing a frequency band in this example.

FIG. 3 is an explanatory diagram showing a division state of a signal space by the discrete wavelet transform. In this FIG.
The horizontal axis represents time, and the vertical axis represents frequency, and shows how the signal space is divided in both the time and frequency directions by the discrete wavelet transform. That is, in FIG.
The frequency space is from level M to level N (= M +
Until 3), it is divided into four levels. In the time space, the time of the level M is twice the length of the level M + 1, the time of the level M + 1 is twice the length of the level M + 2, and the time of the level M + 2 is the length of the level N (= M + 3). It is divided so as to be twice as long.

FIG. 4 is an explanatory diagram showing each function used in the discrete wavelet transform. The scaling function of discrete Waveland wavelet transform and phi, when the corresponding Waveland let [psi "basis functions" in phi is given, the level i, and space V _i spanned phi of (2 (i) x-k ), ψ (2
(I) x-k) Hull determines space W _i, and any function f _i space V _i, the space W _i arbitrary function g _i, Equation 1 and Equation 2
It is represented in the form of Then, the function f _i can be uniquely decomposed as in Expression 3. Also, the reconstruction of the wavelet transform is to find the left side from the right side of Equation 3, which is obtained by Equation 4. It should be noted that, regarding such a discrete wavelet transform, only a portion related to the present invention will be described. Since it is detailed in his book, it is omitted here.

Next, a method of generating a noise waveform according to the present embodiment will be described with reference to the flowcharts of FIGS. FIG.
FIG. 6 is a flowchart showing an outline of a noise waveform generation method according to the present embodiment. FIG. 6 is a flowchart showing steps S2 and S3 in FIG.
5 is a flowchart showing details of an operation performed repeatedly at each time. First, each step in these flowcharts will be described. In FIG. 5, S1 is a step of weighting each divided band, and S2 is a step of generating noise using a random number for each band.
S3 is a step of generating the entire noise waveform by synthesizing the noise generated in S2, and S4 is a step of advancing time. Then, S5 is a step of determining whether or not it is the end time.

Next, in FIG. 6, S11 is a step of setting M to a variable i indicating the level, and S12 is a step of determining whether or not the coefficients c _i and d _i of the level _i are set. S13. A determining whether the level i is N + 1 is smaller than, S14 is a step of setting the weighted random number in d _i. Also, S1
5 is a step of calculating c _i from c _i-1 and d _i-1,
S16 is a step of incrementing the level variable i. Then, S17 is a step of determining whether or not i is larger than N.

Next, the noise generation operation of this embodiment will be described in detail based on such a flowchart. First, in step S1 of FIG. 5, for example, a band corresponding to a frequency characteristic as shown in FIG. 2 is divided into non-overlapping frequency bands, and weighting of each band is determined so as to approximate a desired characteristic. As an approximation method for each band, the band may be approximated by a gain at one point such as a median value, or may be approximated by an average value of a plurality of points.

Thereafter, in step S2 in FIG. 2, the above-mentioned weighted random numbers are generated for each band, and a noise waveform having a frequency component of each band is generated. Next, in step S3 of FIG. 2, the noise waveform of each band is synthesized,
Generate the overall noise waveform. Steps S2 and S3 above
Is repeatedly executed for each time step. The weighted random number is generated by multiplying a random number having a normal distribution with an average of 0 and a variance of 1 by a coefficient corresponding to the weighting.

Next, the details of the operations in steps S2 and S3 will be described.
Details will be described with reference to FIG. Here, as shown in FIG.
M is the lowest level of the frequency band to be considered and M is the highest level.
Let N be the bell. Also, a variable representing a level is represented by i, and
In 6, first, i is set to M (S11). Soshi
Therefore, in S12 of FIG. 6, the discrete wavelet transform
Coefficient i of level i _iAnd d_iJudge whether is already set
You. Whether the values of each coefficient c and d have already been set
Is determined using a flag. Where the discrete wave
Coefficient c of level i_iAnd d_iIs still set
If not, perform the following processing.

First, when i is smaller than N + 1, (S1
3) A random number is generated, and d _i is set by performing weighting set for each band set in step S1 of FIG. 5 (S14). Next, using Equation 4 to calculate the values of the coefficients c _i from one level lower value of the coefficient c _i-1 and d _i-1 (S1
5). Next, the level variable i is incremented, and the values of c and d of the upper level are set (S16). By repeating the above processing from level M to level N, the values of coefficients c and d from level M to level N are set, and finally c _{N + 1} of level N + 1 is obtained. Level i
And i + 1, the time interval of i + 1 is 1 of i
/ 2, the number of random numbers generated is twice i.

As described above, steps S2 and S
3 is repeated for each time step to synthesize a value of the coefficient c _{N + 1} of the level N + 1, thereby generating a waveform in which noise of each band is synthesized. That is, a noise waveform synthesized using the value of the coefficient c _{N + 1} is output. As described above, according to the present embodiment, it is possible to generate an aperiodic noise waveform while generating random numbers sequentially for each band without using a filter.

Next, another embodiment of the present invention will be described. FIG. 7 is a flowchart showing details of the operation repeatedly performed at each time in steps S2 and S3 of FIG. 5 in another embodiment of the present invention. First, each step in this flowchart will be described. In FIG. 7, S2
1 is a step of setting M to a variable i indicating the level, and S22 is a step of determining whether or not the coefficient di of the level _i is set. Also, S23 is a step of setting a weighted random number d _i, S24 is a step of incrementing the level of variable i.
S25 is a step of determining whether i is greater than N, and S26 is a step of setting M to a variable i indicating the level. S27 is a coefficient c of level i.
determining whether _i is set,
S28 is a step of calculating c _i from c _i-1 and d _i-1. S29 is a step of incrementing the level variable i, and S30 is a step of determining whether i is greater than N + 1.

Next, the noise generation operation of this embodiment will be described in detail based on such a flowchart. In this example, first, a value of d is generated for each level, and then a value of c is generated. Here, as in the example shown in FIG. 6, the lowest level of the frequency band to be considered is M, and the highest level is N. Further, a variable representing the level is set to i, and first, i is set to M (S21). When the coefficients d _i at level i of the discrete Waveland wavelet transform has not yet been set (S22) performs the following processing.

[0023] First, a random number is generated to set by weighting set for each band set in step S1 of FIG. 4 the coefficient d _i (S23). Next, the level variable i
Is incremented, and the value of the coefficient d of the upper level is set (S24). By repeating the above process from level M to N, the value of each coefficient d from level M to level N is set. Next, the value of the coefficient c is generated. First, i is set to M (S26). When the coefficient c _i of level i of the discrete Waveland wavelet transform has not yet been set (S27) performs the following processing.

Firstly, using equation 4, to calculate the value of the coefficient c _i from one level lower value of the coefficient c _i-1 and d _i-1 (S2
8). Next, the level variable i is incremented (S2
9) Set the value of c at the upper level. By repeating the above processing from level M to N + 1, the values of c and d from level M to level N are set, and finally the coefficient c _{N + 1} of level N + 1 is obtained. That is, the coefficient c
A noise waveform synthesized using the value of _{N + 1} is output. As described above, according to the present embodiment, it is possible to generate an aperiodic noise waveform while generating random numbers sequentially for each band without using a filter. It should be noted that the present invention is not limited to the above-described embodiments, and it is apparent that the present invention can be appropriately modified within the scope of the technical idea of the present invention.

[0025]

As described above, in the noise waveform generating apparatus according to the present invention, the frequency band corresponding to the desired frequency characteristic is divided into a plurality of non-overlapping bands by the discrete wavelet transform. And the setting means sets the magnitude of the noise in each band so as to approximate the desired frequency characteristic, generates a random number weighted for each band, and uses the noise generation means to set the basis function in the discrete wavelet transform. The noise of the magnitude set for each band is generated by setting the coefficient by a random number, and the synthesis unit synthesizes the noise for each band. Therefore, there is an effect that a noise waveform having desired characteristics can be easily generated without using the filter theory or the approximation theory.

In the noise waveform generating method according to the present invention, a frequency band corresponding to a desired frequency characteristic is divided into a plurality of non-overlapping bands by using discrete wavelet transform. Set the magnitude of noise in each band to approximate the characteristics Generate random numbers weighted for each band, and set the coefficients of the basis function in the discrete wavelet transform by random numbers Is generated, and noise is synthesized for each band. Therefore, there is an effect that a noise waveform having desired characteristics can be easily generated without using the filter theory or the approximation theory.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a functional configuration of a noise waveform generation device according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram showing an approximation method of a frequency characteristic processed by the generation device shown in FIG. 1;

3 is an explanatory diagram showing a division state of a signal space by a discrete wavelet transform processed by the generation device shown in FIG. 1;

FIG. 4 is an explanatory diagram showing each functional expression used in the discrete wavelet transform processed by the generation device shown in FIG. 1;

FIG. 5 is a flowchart showing a noise generation operation in the generation device shown in FIG. 1;

FIG. 6 is a flowchart showing an operation example for each time step in the noise generation operation shown in FIG. 5;

FIG. 7 is a flowchart showing another operation example for each time step in the noise generation operation shown in FIG. 5;

FIG. 8 is an explanatory diagram showing a conventional noise waveform generation method.

[Explanation of symbols]

10 band dividing means, 20 setting means, 30 noise generating means, 40 combining means.

Claims (4)

(57) [Claims] 1. A band dividing means for dividing a frequency band corresponding to a desired frequency characteristic into a plurality of non-overlapping bands by using a discrete wavelet transform. Setting means for setting the magnitude of noise in each band divided by the band dividing means, noise generating means for generating noise of the magnitude set by the setting means for each band, and noise generating means for generating noise. Synthesis means for synthesizing noise;
And the setting means comprises:
A random number generator that generates random numbers weighted for each band
Wherein said noise generating means comprises said discrete wavelet
The coefficient of the basis function in the conversion is set by the random number.
A means for generating noise in each band by performing the operation . Wherein said noise generating means synthesizes the band of noise waveform of lower level, generator of noise waveform according to claim 1, characterized in that it comprises means for generating a high-level of noise waveform. 3. A frequency band corresponding to a desired frequency characteristic is divided into a plurality of non-overlapping bands using a discrete wavelet transform, and noise in each band is approximated to the desired frequency characteristic. set the size
To generate a random number weighted for each band,
The coefficients of the basis function in the scattered wavelet transform are
A method of generating a noise waveform , wherein a noise having a magnitude set for each of the bands is generated by setting the number, and noise is further synthesized for each band. 4. The noise waveform generation method according to claim 3, wherein a noise waveform of a lower level band is synthesized to generate a noise waveform of an upper level.