JP2001244793A - Notch filter - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a notch filter that eliminates unwanted line spectrum components from a broadband signal, on which the undesired line spectrum component is superimposed, easily adjusts the frequency of the eliminated line spectrum and suppresses only the unwanted line spectrum without attenuating the broadband signal component. SOLUTION: The notch filter is provided with a line spectrum frequency specification means 11, that uses a high-degree prediction filter applying linear prediction analysis to an input signal to specify a frequency of a line spectrum, a sine wave/cosine wave generating means 12 that generates a sine wave and a cosine wave with the same frequency as that of the line spectrum, an adaptive filter 13 that receives the sine wave and the cosine wave as its input signals, and an adder 14 that provides an output of the difference between a signal resulting from superimposing the line spectrum on the broadband signal and an output signal from the adaptive filter 13, and also a means that updates the coefficient of the adaptive filter so as to minimize the output from the adder 14.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a notch filter which removes a line spectrum component from a broadband signal on which an unnecessary line spectrum component such as a power supply hum is superimposed, and extracts only a required broadband signal.

[0002] A notch filter is realized by adjusting the zero point of the filter frequency characteristic to the line spectrum frequency that blocks the passage. FIG. 8 shows the basic structure of the notch filter. 81 and 82 are delay elements for causing a delay of one sampling period, 83 and 84 are multipliers for multiplying coefficients,
85 and 86 are adders.

[0003] The notch filter shown in FIG. 8 is a second-order non-recursive filter, and its zero point frequency f ₀ is determined by a multiplier 8
It is determined by a coefficient a of 3. The relationship between the zero point frequency f ₀ and the coefficient a is expressed by the following equation (1). a = −2√b · cos (2πf ₀ T) (1) where T is a sampling period.

[0004] The blocking characteristic of the notch filter shown in FIG. 8 becomes steeper as the coefficient b of the multiplier 84 is set to a value closer to 1. This means that by setting the coefficient b of the multiplier 84 to a value close to 1 and adjusting the coefficient a of the multiplier 83, the rejection frequency of the notch filter can be easily adjusted.

[0005]

2. Description of the Related Art FIG. 9 shows a frequency characteristic of a second-order acyclic filter, and a solid line shows a frequency characteristic of the acyclic filter shown in FIG. 8 calculated by giving a coefficient a so that a stop frequency becomes 800 Hz. is there. However, the coefficient b is set to b = 1 at which the rejection characteristic is the steepest.

Obviously, in this frequency characteristic, the zero point is 8
At 800 Hz, which blocks the 800 Hz line spectrum from passing. However, its frequency characteristic is not sufficiently steep as can be seen from the figure, and is 800 Hz.
Other frequency components are also greatly attenuated.

As a countermeasure for reducing attenuation of frequency components other than the line spectrum to be blocked, a first-order or second-order recursive filter constituting a pole is usually cascaded to a notch filter. In order to increase the gain of the pass band other than the line spectrum to be rejected, thereby increasing the frequency characteristic of the entire filter.

The dashed line in FIG. 9 indicates that a recursive filter 101 having a transfer function of 1 / (1-√b · z ⁻¹ ) having a pole in the DC component as shown in FIG. 10 is added to a notch filter shown in FIG. It is a frequency characteristic at the time. Obviously, the addition of the recursive filter 101 improves the frequency characteristic of the pass band and sharpens the line spectrum rejection characteristic.

[0009]

There are two problems here. One is that the addition of a recursive filter having a pole loses the linear phase characteristic (phase lag characteristic proportional to frequency) which is an advantage of the non-recursive filter. The other is that the components of the broadband signal to be passed are also attenuated at the same frequency as the line spectrum to be removed.

Further, as an important application example of the notch filter, there is a case where the frequency of a line spectrum to be removed is unknown. In this case, a mechanism for automatically calculating the coefficient a is required. This calculation is typically using an adaptive algorithm for example learning identification method, the coefficient a is set at time j is expressed as a _j, the following equation _{(2) a j + 1 =} a j + μe j x j-1 / is performed by ^{_{(x j-1 2 + x}} j-2 2) approaches closer sequential coefficients a _j performs an operation of (2) the coefficient a.

Here, μ is a constant called a step size.
Number and other variables e_j, X _j-1, X_j-2Figure 8
For each signal in the non-recursive filter shown in_jIs acyclic
The output signal of the round filter, x_j-1Is the input signal x_jOne of the
Delay signal for the regularization cycle, x_{j- Two}Is the input signal x_jTwo specimens
This is a delay signal for the conversion cycle.

This adaptive algorithm converges the coefficient a _j to a so as to minimize the output signal e _j . Therefore,
If the input signal is a line spectrum, the coefficient a _j is converged to a value a of the formula (1) described above, the passage of the line spectrum of the frequency f ₀ when the output signal e _j becomes minimum blocking Is done.

That is, by applying the above adaptive algorithm, the non-recursive filter shown in FIG. 8 forms a notch filter that removes the line spectrum of the input line spectrum in accordance with the frequency of the line spectrum.

However, two problems are pointed out in such a notch filter. First, regarding the arrangement of poles for flattening the frequency characteristics of the passband so that frequency components other than the line spectrum near the zero point are not attenuated, an effective method of this arrangement has not yet been established. Absent.

The other occurs when a plurality of line spectra are blocked. In this case, it is necessary to cascade and use a plurality of second-order acyclic filters corresponding to a plurality of line spectra. However, the adaptive algorithm, only the frequency characteristic of the output signal e _j updates the coefficients of each FIR filter so that the flat, do not necessarily constitute the notch filter that matches the zero point in the frequency line spectrum . In other words, it is very difficult to form a notch filter that blocks the passage of a plurality of line spectra with the conventional notch filter configuration method.

An object of the present invention is to maintain the easiness of adjusting the line spectrum frequency to be rejected, to leave the line spectrum of unknown frequency without attenuating the broadband signal component, and to suppress only the line spectrum component. It is an object of the present invention to provide a notch filter having a new structure.

[0017]

A notch filter according to the present invention comprises: (1) a notch filter for removing a line spectrum superimposed on a wideband signal, wherein the sine wave generates a sine wave and a cosine wave having the same frequency as the line spectrum; A cosine wave generating means, an adaptive filter using the sine wave and cosine wave generated by the sine wave / cosine wave generating means as input signals, a signal in which a line spectrum is superimposed on the wide band signal, and an output signal of the adaptive filter And an adder for outputting a difference from the adaptive filter, and means for updating the coefficient of the adaptive filter so that the output of the adder is minimized.

(2) The notch filter includes a line spectrum frequency specifying means for specifying a frequency of a line spectrum by a higher-order prediction filter for performing a linear prediction analysis on an input signal, wherein the sine wave / cosine wave is provided. The generating means is for generating a sine wave and a cosine wave having the frequency specified by the line spectrum frequency specifying means.

(3) The predictive filter in the line spectrum frequency specifying means reads out a sine wave waveform value stored in advance and multiplies it by a coefficient of the predictive filter to calculate a spectral envelope of an input signal. The frequency specifying means specifies a maximum point of the spectrum envelope of the input signal and determines the frequency of the line spectrum.

[0020]

FIG. 1 is a diagram illustrating the principle of a notch filter according to the present invention. The notch filter according to the present invention includes a line spectrum frequency specifying unit 11 for specifying a frequency of an input line spectrum, and a sine wave / sine wave for generating a sine wave and a cosine wave corresponding to the frequency of the specified line spectrum.
It comprises a cosine wave generating means 12, an adaptive filter 13 using the sine wave and the cosine wave as reference signals, and an adder 14 for calculating a difference between an output signal of the adaptive filter 13 and an input signal.

The notch filter according to the present invention has solved the above-mentioned problem by separately providing means for specifying the frequency of the line spectrum and means for removing the line spectrum. In other words, the separation of the two means eliminates the need to simultaneously specify the frequency of the line spectrum and adjust the zero-point frequency, and the frequency of the line spectrum can be specified independently. Various means can be utilized.

As one example, for example, a general harmonic analysis [N. Wiener, “The Fourier Integraland Certain of I
ts Applications ”Dover Publication Inc. (1958)], which subtracts the sine wave from the input signal within a certain observation interval, and reduces the sine wave so that the difference result is minimized. Number, frequency, phase,
This is a method in which the amplitude is adjusted and the input signal is represented as a combination of sine waves.

By using this method, the line spectrum frequency of the input signal can be accurately calculated although it takes some time. However, if the line spectrum frequency is known, it goes without saying that this means is not necessary.

Next, the system identification system shown in FIG. 2 and the configuration of the present invention are considered in association with each other. First, a sine wave and a cosine wave having the same frequency as the frequency of the line spectrum specified by the general harmonic analysis or the like are generated, and correspond to the reference signal _Sj in the system identification system of FIG.

[0025] is observed as an unknown system 20 (multiplied by a constant) amplitude change with respect to its reference signal S _j, signal x _j superimposed wideband signal n _j in the unknown system output. Here, assuming that the wideband signal n _j and the reference signal S _j can be assumed to be independent of each other, the coefficients of the adaptive filter 21 are updated so as to cancel the unknown system output and minimize the residual E _j .

[0026] to correspond to the configuration operation is shown in figure 1, one input of the adder 14 shown in the FIG. 1 is the sum x _j of the unknown system output wideband signal n _j, the adaptive filter 1
The sine wave and cosine wave supplied to 3 correspond to the reference signal _Sj .

Therefore, in the configuration shown in FIG. 1, if the coefficient of the adaptive filter 13 is updated so that the output of the adder 14 becomes small, a line corresponding to the reference signal _Sj in the system identification system shown in FIG. A notch filter that removes only the spectral components is configured.

As a specific example of the signal input to the present invention,
Assuming that a plurality of line spectrum signals to be superimposed on the wideband signal n _j are g _j = Σ _{k = 1} ^K cos (2πf _k jT + θ _k ) (3), K = 32, α _k = 1.0 , F _k = 102k +
An example of the operation when the present invention is applied to a signal superimposed at a power ratio of 20 dB using the wideband signal n _j as white noise and given as 400, θ _k = π / 4 and T = 1/8000 will be described.

Further, a linear prediction analysis is used to specify the frequency of the line spectrum. In the above equation (3) and the like, the symbol “Σ _{k = 1} ^K ” means that the right term of k is added as 1 to K.

[0030] First, as a line spectrum frequency specifying means 11, the input signal x _j wideband signal n _j to line spectral group g _j is superimposed, the linear prediction analysis using the prediction filter having a sufficiently high degree When executed, the spectral envelope of the input signal x _j is obtained by changing the shape as the coefficient of the pre-filter.

FIG. 3 shows the configuration of a linear prediction filter of order M. The spectral envelope of the input signal x _j is given as a coefficient H (m) (m = 1 to M) of the prediction filter (this is an original function of the linear prediction analysis), and the prediction residual ε of the linear prediction filter is obtained. _{When j} becomes the minimum, each coefficient H (m) of the prediction filter represents the spectral envelope of the input signal.

Therefore, the spectrum envelope of the input signal x _j is obtained as the coefficient H (m) of the prediction filter,
From the spectral envelope, the frequency of the line spectrum is calculated as its maximum. Then, a sine wave and a cosine wave having the same frequency as the calculated line spectrum frequency are generated by the sine wave / cosine wave generation means 12.

FIG. 4 shows a spectral envelope S (f) of an input signal x _j calculated from coefficients obtained by performing linear prediction analysis using a learning identification method, using a non-recursive filter of order M = 256 as a prediction filter. Is shown. However, for the calculation, the coefficient H (m) of the prediction filter is calculated by the following equation (4) S (f) = { _{m = 1} ^M {H (m) · exp (−iπmfT)} (4) It is done by substituting.

In this calculation, s in equation (4) is used.
It is not necessary to actually calculate in (2πmfT) and cos (2mfT). For example, when specifying the frequency with an accuracy of 1 Hz, the waveform value of a 1 Hz sine wave is sampled at a sampling period T
Each time, it is calculated in advance and stored in a memory, and sin (2πmfT) is obtained by reading out the waveform value every m intervals, and cos (2πmfT) is obtained by reading out the waveform value by shifting by ４ period. .

Further, the sine wave waveform value actually stored is 1
It is not necessary to store the half cycle or the quarter cycle, the reading order is controlled, and the waveform value of the half cycle or the quarter cycle is repeatedly read out. Can be taken out.

Next, as an example of a wideband signal, the transfer function is given by the following equation (5): F (z) = 1 / {1−γ cos (2πf _a T) z ⁻¹ + γ ² z ⁻² } ( provides an output signal w _j obtained in the secondary cyclic type filter becomes 5) enter the white noise, the superimposed signals x _j line spectrum g _j described above in the signal.

The transfer function F (z) of equation (5)
The next recursive filter includes adders 51 and 52 shown in FIG.
Multiplied by _a coefficient γcos (2πf _a T)
, A multiplier 54 for multiplying by a coefficient (−γ ² ), and delay elements 55 and 56 having one sampling period. The signal x _j is obtained from the output of the adder 57 that adds the output signal w _j of the second-order recursive filter of the transfer function F (z) and the line spectrum g _j .

[0038] FIG. 6 is a line spectrum g _j to the wideband signal w _j
There against superimposed signals x _j, depicts a spectral envelope calculated from the coefficients of a prediction filter. Where f _a =
960 Hz, γ = 0.98, and order M = 2048
To enhance the separation between the line spectrum g _j and the wideband signal w _j .

Then, the frequency g _j of the line spectrum is specified by the line spectrum frequency specifying means 11 from the maximum point of the spectrum envelope shown in FIG. 6, and the sine wave and cosine wave of the frequency g _j are generated by the sine wave / cosine wave generating means. 12 is generated by the coefficients of the adaptive filter 13 for the sine wave and cosine wave, the output of the adder 14 for calculating a difference between the output and the input signals x _j of the adaptive filter 13 is adjusted so as to minimize , The broadband signal from which the line spectrum has been removed is output from the adder 14.

[0040] Figure 7 shows the spectral envelope to be output to the above wideband signal w _j and line spectrum g _j and is superimposed input signals x _j, from the notch filter according to the present invention. As is clear from FIG. 7, the superimposed line spectrum is removed, and the same frequency component as the line spectrum frequency of the broadband signal is output without being attenuated and stored.

[0041]

As described above, according to the present invention,
By separately configuring the means for specifying the frequency of the line spectrum that blocks passage and the means for removing the line spectrum, it is possible to easily adjust the line spectrum frequency to be blocked and to remove the line spectrum. For a signal other than the power line spectrum, a notch filter that suppresses only unnecessary line spectra without attenuating the same frequency components as the line spectrum to be blocked is obtained.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating the principle of a notch filter according to the present invention.

FIG. 2 is a diagram showing a correspondence between a system identification system and a configuration of the present invention.

FIG. 3 is a diagram illustrating a configuration of a linear prediction filter of order M.

FIG. 4 is a diagram illustrating a spectrum envelope of an input signal given from coefficients of a prediction filter.

FIG. 5 is a diagram illustrating a specific example of generating a wideband signal.

FIG. 6 is a diagram illustrating a spectrum envelope given from coefficients of a prediction filter for a signal in which a line spectrum is superimposed on a wideband signal.

FIG. 7 is a diagram showing a spectrum envelope output from a notch filter according to the present invention.

FIG. 8 is a diagram showing a basic structure of a conventional notch filter.

FIG. 9 is a diagram illustrating frequency characteristics of a second-order acyclic filter.

FIG. 10 is a diagram showing a configuration in which a first-order recursive filter constituting a pole is cascadedly arranged in a notch filter.

[Explanation of symbols]

 11 Line spectrum frequency specifying means 12 Sine wave / cosine wave generating means 13 Adaptive filter 14 Adder

Claims (3)

[Claims] 1. A notch filter for removing a line spectrum superimposed on a wide-band signal, comprising: a sine / cosine wave generating means for generating a sine wave and a cosine wave having the same frequency as the line spectrum; An adaptive filter that uses a sine wave and a cosine wave generated by the means as input signals, and an adder that outputs a difference between a signal obtained by superimposing a line spectrum on the broadband signal and an output signal of the adaptive filter. A notch filter comprising means for updating the coefficient of the adaptive filter so that the output of the adder is minimized. 2. The notch filter includes a line spectrum frequency specifying unit that specifies a frequency of a line spectrum by a higher-order prediction filter that performs a linear prediction analysis on an input signal, and the sine wave / cosine wave generation unit includes: 2. The notch filter according to claim 1, wherein a sine wave and a cosine wave having a frequency specified by the line spectrum frequency specifying means are generated. 3. A predictive filter in the line spectrum frequency specifying means reads out a sine wave waveform value stored in advance and multiplies it by a coefficient of the predictive filter to calculate a spectrum envelope of an input signal. 3. The notch filter according to claim 2, wherein specifies a maximum point of a spectrum envelope of the input signal and determines a frequency of a line spectrum.