KR19980087722A - An adaptive finite impulse response filter of a generalized subband decomposition structure using a wavelet transform and a subfilter with a diadic sparse factor - Google Patents

Abstract

It is an object of the present invention to provide a method and apparatus for performing a wavelet transform which has excellent convergence characteristics and a reduction in computation amount for input signals such as channel equalization and periodic noise cancellation using a digital adaptive filter, And to provide an adaptive finite impulse response (FIR) filter of band decomposition structure.

According to an aspect of the present invention, there is provided an adaptive FIR filter comprising: an interpolator for converting an interpolator and a subfilter portion into a uniform band in a subband decomposition structure; A wavelet transformer having an octave band characteristic and a sub-filter having a dyadic sparse factor according to a frequency band of the interpolator.

Description

An adaptive finite impulse response filter of a generalized subband decomposition structure using a wavelet transform and a subfilter with a diadic sparse factor

The present invention relates to an adaptive filter of a generalized subband decomposition structure among digital adaptive filters in the field of electrical and electronic engineering. More particularly, the present invention relates to an adaptive filter having an excellent convergence characteristic for an input signal when channel equalization and periodic noise elimination using an adaptive filter, And an adaptive finite impulse response (F1R) filter of a generalized subband decomposition structure using a subfilter having a diadic sparse factor.

In the adaptive filter, adaptive processing can be divided into a block processing method and a real-time processing method according to a weight updating cycle. The block processing method is a method of converting an input signal into a block, independently updating each weight, and then performing inverse transformation, and the conversion, weighting and updating of the input signal and the request signal are performed on the signal of one block and the inverse conversion of the weighted value is performed There is an advantage that the number of operations is smaller than the real-time processing method. However, since one block of signal is received and processed, there is a disadvantage that the time delay of one block between the output and the input becomes slow and the convergence speed is slow.

The real-time processing method is a method of processing input signals in a sample period, and there is a disadvantage in that the number of operations is large because the input samples are transformed, weighted, and updated. However, there is an advantage that the input is output immediately and the convergence speed is fast.

The adaptive filter can be divided into an F1R and an IIR (infinite impulse response) adaptive filter as an impulse response of the transfer function depending on the presence or absence of feedback. The FIR adaptive filter has the advantage that it is always stable system because there is no feedback, and the structure is simple. However, there is a disadvantage that the computation amount increases when a high order filter is required. The IIR adaptive filter has a problem of instability due to the feedback, but the transmission characteristic required of the adaptive filter is advantageous in that it can be implemented with a smaller amount of computation than the FIR adaptive filter.

In addition, the adaptive filter can be divided into a transversal type and a lattice type. The transversal type is called a direct type or a tapped delay line (TDL) type because the structure is simple and widely used because the transfer function is expressed simply. Although the lattice type has a complicated structure, the stability of the filter can easily be expressed by the coefficients, and the frequency response of the transfer function is not sensitively changed according to the change of the coefficients.

In general, the adaptive filter is an FIR adaptive filter which is a stable system, and a transversal type whose structure is simple is mainly used, and it is divided into a time domain and a conversion domain depending on the processing domain. The adaptive filter of the transform domain has the advantage of faster convergence speed than the time domain adaptive filter, but it has a disadvantage that it requires a lot of computation when the order of the filter is large because the transform of the same size as the filter order is processed every time the input is applied. This disadvantage can be solved by using a structure that decomposes an FIR filter into subbands, with a transform size smaller than that of the filter.

FIG. 1 is a block diagram of a conventional generalized subband decomposition adaptive FIR filter. The adaptive FIR filter includes a delay 2 for sequentially outputting an input signal x (n) (1) in a delayed manner, An interpolator 3 of an M-point uniform transform matrix for receiving and converting a signal to generate an output signal u ₀ (n) - u _M-1 (n), a FIFO A memory function buffer memory 4, a uniform sparsity factor (USF) sub-filter 5 for calculating the output data of the buffer memory for each band in accordance with an adaptive control signal of the computer, (N) 6 of the sum signal by summing the outputs of the sub-filters, and a subtractor 9 for subtracting the output signal y (n) (10) for generating an error value e (n) between the adder (10) and the adder (10) And a computing unit (8) provided to generate an adaptive control signal for each of the structural units of the sub-group filter USF.

Here, the output of the delay 2 is shifted each time the input signal x (n) is input, and the M input signals x (n)

.

The interpolator 3 uses a transform size M smaller than the filter order N and uses an orthogonal transform to transform it into a uniform band such as DFT (Discrete Fourier Transform). When the transform matrix of the interpolator 3 is set to T, the transformed output u (n)

. here

to be.

FIG. 2 is a diagram showing the relationship between the buffer memory 4 and the USF sub-filter 5. Here, the buffer memory 4 has a first in first out (FIFO) memory structure for sequentially storing the output signals of the equation (3) converted by the interpolator 3 according to the converted moments, It is used in the calculation of the output equation and in the process of obtaining the expected value of the converted signal power.

The USF subfilter 5 can use a value L (M) less than or equal to the conversion size M, and the number of coefficients of the sparse subfilter in each branch is K The total equivalent order of this adaptive filter is equal to N = (K-1) L + M.

If the coefficient matrix of all the M sub-filters with the sparse parameter L is G

to be.

The coefficients of the sub- }, The row vector is the coefficients of the k sub-filters, and the row vector is the Lt; th > The sub-filter in the kth branch silver

to be.

Then, Weight vector representing the < RTI ID = 0.0 > silver

to be.

The values stored in the buffer memory and the Using the weighted vector of coefficients, the filter output y (n)

to be.

That is, the value of the output signal y (n) (6) Th coefficients It is the sum of the inner products of the values converted and stored L times ago.

The operator 8 newly updates the coefficients of the sub filter by using the error signal e (n) which is the difference between the demand signal d (n) 7 and the filter output signal y (n) 6 by the adaptive algorithm, May be a least mean square (LMS) or the like.

This conventional subband decomposition adaptive FIR filter is limited to the division of the interpolator into uniform bands, and the sparse factor of sparse subfilters is used with the same value as given condition (L? M).

3 shows an example of frequency response of each of eight branches of the sub-filter when L = M = 8 in the conventional subband decomposition adaptive FIR filter. Here, (1) is the desired response that is selected as the passband of the interpolator, and the remaining region except (1), that is, the region of (2), is an unwanted image caused by a rare factor.

If the sparse factor L is set to L> M, there will be L-1 image frequency bands. However, since the passband of the interpolator is divided into 1 / M due to the conversion size M, an unwanted virtual band is included in the subfilter band corresponding to the passband of the interpolator. Therefore, the sparse factor of each subfilter uses a value less than or equal to the frequency response of this adaptive filter divided by the passband of the interpolator.

As can be seen, the frequency bandwidth of the interpolators by the DFT is uniform, and therefore the subfilter in each branch can be constructed with a USF subfilter. If the interpolator is composed of a discrete wavelet transform in the USF subfilter, the frequency bandwidth of the interpolators varies depending on the level, so that the total frequency response of the subband decomposition adaptive filter is different from the desired frequency response due to the unwanted image band .

FIG. 4 shows that the frequency band of the wavelet transform shows an octave band characteristic when a discrete wavelet transform (transform size M = 8) is applied to the interpolator. Here the number of levels is J = And has a band pass level and a low DC level or L (-1) level.

When using a subfilter as a homogeneous sparse factor when using a wavelet transform with an interpolator, the sparse factor should be less than or equal to 2 at the highest level using the widest band, as mentioned above. If L = M is used in a condition where the sparse factor is less than or equal to the transform size (L M), the L (-1) and L (0) levels do not cause a problem, The frequency response characteristic of the adaptive filter will be changed.

For example, suppose that an example of the frequency response after the adaptation is completed in the adaptive filter is shown in FIG. 5, where a wavelet transform is used as an interpolator and a conventional uniform sparse factor is used in the sub- 8), the frequency band of the branch corresponding to the L (1) level of the interpolator is up-sampled by 2 times as high as π / 4 and the sparse factor is 8 from π / 4 to π / 2, As shown in FIG. 6, the entire frequency response of the adaptive filter is changed in its characteristics, so that the operation frequency of the operation filter of the adaptive filter 8) becomes large, and consequently the convergence speed becomes slow.

It is an object of the present invention to solve the problem of lowering the convergence speed in the conventional adaptive filter as described above and to improve the convergence speed and the reduction of the computational complexity for the input signal in the case of channel equalization and periodic noise elimination using the digital adaptive filter, And an adaptive finite impulse response (FIR) filter of a generalized subband decomposition structure using a wavelet transform and a subfilter with a diadic sparse factor.

1 is a block diagram of a conventional generalized subband decomposition adaptive FIR filter.

2 is a block diagram showing the relationship between a buffer memory and a subfilter in a conventional adaptive FIR filter.

3 is a frequency response characteristic diagram of a conventional sub-filter composed of a uniform scarcity factor.

4 is a diagram illustrating a frequency band when wavelet transform is used for the interpolator.

5 is a waveform diagram of an exemplary frequency response of an adaptive filter.

FIG. 6 is a frequency response characteristic diagram of a subfilter in which wavelet transform is used as an interpolator and a rare factor is uniformly formed.

FIG. 7 is a block diagram of a subband decomposition adaptive FIR filter composed of a diamond sparse factor according to the present invention.

8 is a diagram showing the relationship between the buffer memory and the subfilter in the adaptive FIR filter of the present invention.

9 is a detailed block diagram of a buffer memory and a subfilter of the present invention.

FIG. 10 is an internal detailed structural diagram of the coefficients and calculation blocks of FIG. 9; FIG.

FIG. 11 is a frequency response characteristic diagram according to the level of sub-filters constituted by a diamond scar factor according to the present invention.

12 is a configuration diagram of a periodic noise canceller using a DWT-DSFS FIR adaptive filter according to the present invention.

13A and 13B are graphs of convergence characteristics when the noise period of the periodic noise eliminator of FIG. 12 is 12.8 samples and 2 samples, respectively.

FIG. 14 is a diagram illustrating a configuration of a channel equalizer using a DWT-DSFS FIR adaptive filter according to the present invention.

15 is a graph of convergence characteristics of the channel equalizer of Fig.

16 is a diagram illustrating an example of a system modeling configuration using a DWT-DSFS FIR adaptive filter according to the present invention.

17 is a graph showing the convergence characteristic of the system modeling of Fig.

[Description of Reference Numerals]

1: input signal

2: retarder

3: uniform conversion interpolator

3 ': wavelet transform interpolator

4: buffer memory

5: USF sub-filter

5 ': DSF sub-filter

6: Output signal

7: Request signal

8: Operator

9,10: Totalizer

: transfer function of the subfilter in branch k (where Lt; / RTI >

u (n): the signal transformed at the interpolator when n (time)

u (n-L): The signal converted before L times before n

: n When the subfilter field Th coefficient (weighted vector)

M: Transformation size.

N: Order of the filter.

In order to achieve the above object, the adaptive FIR adaptive filter of the subband decomposition structure of the present invention finds a method of making the sparse factor of the subfilter different according to the wavelet transform level, And a sub-filter having a diamond scarring factor is constructed so as to coincide with the pass band.

Hereinafter, the present invention will be described in detail.

FIG. 7 is a block diagram of an FIR filter which is an object of the generalized subband decomposition structure using the wavelet transform and the sub-filter having a diamond dotarity factor according to the present invention. The input signal x (n) (1) And a M-point discrete wavelet transformer for receiving the time domain signal from the delay and generating an output signal u ₀ (n) - u _M-1 (n) a buffer memory 4 for temporarily storing a wavelet transform signal of the interpolator and a buffer memory 4 for storing a wavelet transform signal of the interpolator; A dyadic sparsity factor (DSF) sub-filter 5 'for performing an arithmetic processing on each band in accordance with the adaptive control signal, an output signal y (n) corresponding to the input signal by summing outputs of the DSF sub- A summer 9 for generating a summer 6, (10) for generating an error value e (n) between the output signal y (n) of the adder 10 and the request signal d (n) 7 of the adder 10, And an operator (8) for generating an adaptive control signal for each constituent unit of the DSF subfilter and providing the adaptive control signal to the subfilter.

The wavelet transform has localization of the time and frequency domain, and the wavelet transformed value of the signal has time and frequency information at the same time. This is particularly useful for singularity detection and nonstationary processing in combination with the multiresolution theory.

The wavelet transform is performed using a KL (Karhunen- ), The autocorrelation matrix of the transformed signal is concentrated to almost diagonal elements, and the eigenvalue ratio is reduced by preconditioning, and thus the convergence speed is improved in the adaptive filter.

The subfilter transfer function at the kth branch of the DSF subfilter, which is composed of a diamond sparse factor such that the frequency band of the wavelet transform is equal to the desired band of the subfilter, silver

to be.

Where N is the order of the filter, M is the transform size, Is the wavelet transform level at which the k branches belong = -1, 0, 1, ... , J -1) and J = And, k is the marker of the sub-band (k = 0, 1, ... , M -1) , and Is a rare factor (level It is different according to. However, = 0), Lt; RTI ID = 0.0 > k < It is the car coefficient.

In the case where a wavelet transform is applied to the interpolator according to the present invention and a subband decomposition structure adaptive FIR filter is composed of a sub-filter having a diamond scarf factor in the sparse sub filter, a delay unit 2, which can be composed of a shift register, The delayed output of the coarse input signal x (n) (1) is input to the interpolator 3 'and converted by the DWT matrix T to be u _k (n) .

That is, the vector u (n)

to be. here

to be.

The transformed vector u (n) is stored in the buffer memory 4, which is used in the calculation of the output equation and the process of obtaining the expected value of the converted signal power by the moving average.

The filter output y (n)

to be.

here, In the coefficient matrix G of the sub-filter, Th coefficient. In other words,

to be.

The output value of this filter is u (n-2 ) With vectors Th weighted vector It is the sum of the internal things of and.

u (n-2 ) Vector is stored in the buffer memory 4 and the coefficients of the DSF sub-filter 5 'are schematically shown in FIG.

Since the weighting vector of Equation (13) is not uniform in the sparse factor of the sub-filter, There is also a place where there is no coefficient, but an element without a coefficient is also shown for the generalization of the equation.

The error signal e (n)

to be. Where d (n) is the request signal.

For example, the weighted vector update equation using the LMS algorithm

to be. here = 0, 1, ... N / 2-1 , and [mu] is the step size.

Is an M x M diagonal matrix having inverse elements of the power expected values of the converted signals stored in the buffer memory as elements.

FIG. 9 is a detailed configuration diagram of a circuit composed of the buffer memory 4 and the sub-filter 5 'of FIG. 8 when M = 8 . As will be note here, one wavelet transformed M from the group interpolation, i.e., eight input signal _{(u 0 (n), u} 1 (n), u 2 (n), ... u 7 (n),) Lt; RTI ID = 0.0 > M, < / RTI & (N) / E [U _K (n) ² ]], and the coefficient value of the corresponding filter coefficient block is updated .

Of the eight wavelet transformed input signals u ₀ (n), u ₁ (n), u ₂ (n), ... u ₇ (n), from the interpolator, The input signals u ₄ (n), u ₅ (n), u ₆ (n) and u ₇ (n) of the second buffer memory block 4-1 ¹⁾ via the signal _{(u 4 (n-2)} , u 5 (n-2), u 6 (n-2), u is a delay ₇ (n-2)), the second filter coefficient block (5 2) of four filter elements ( : ) To be inputted, these input signals are the output of the computing unit (8) {2μ e (n ) / E [U 4 (n) 2], 2μ e (n) / E [U 5 (n) 2], 2μ E (n) / E [U ₆ (n) ² ], and ² e (n) / E [U ₇ (n) ² ]} to update the coefficient values of the corresponding filter coefficient block.

The delay input signals u ₂ (n-4), u ₃ (n-4) and u ₂ (n-4), which have passed through the two-stage delay circuits of the first buffer memory block 4-1 and the second buffer memory block 4-2, , six of the filter element _{u 4 (n-4),} u 5 (n-4), u 6 (n-4), u 7 (n-4)) is a third filter coefficient block (5-3) ( ) To be inputted, these input signals are the output of the computing unit (8) {2μ e (n ) / E [U 2 (n) 2], 2μ e (n) / E [U 3 (n) 2], 2μ e (n) / E [U 4 (n) 2], 2μ e (n) / E [U 5 (n) 2], 2μ e (n) / E [U 6 (n) 2], 2μ e ( n) / E [U ₇ (n) ² ]} to update the coefficient value of the corresponding filter coefficient block.

The delay input signal u ₄ (n-1) through the two-stage delay of each of the first buffer memory block 4-1, the second buffer memory block 4-2 and the third buffer memory block 4-3, 6), u ₅ (n-6), u ₆ (n-6), u ₇ (n-6)) of the fourth filter coefficient block 5-4 ) To be inputted, these input signals are the output of the computing unit (8) {2μ e (n ) / E [U 4 (n) 2], 2μ e (n) / E [U 5 (n) 2], 2μ E (n) / E [U ₆ (n) ² ], and ² e (n) / E [U ₇ (n) ² ]} to update the coefficient values of the corresponding filter coefficient block.

The converted input signal, that is, the Wavelet-transformed signal, input from the top, has the coefficients shown in detail in FIG. 10, Lt; RTI ID = 0.0 > subfilter < / RTI >

The block {2μ e (n) / E [U _K (n) ² ] at the bottom of FIG. 9 corresponds to a computing unit 8 having an adaptive algorithm. The converted input signal u n-2 )) To process Equation 15 to update the values of the coefficients.

The configuration of the buffer memory 4 and the subfilter 5 'is constituted by repeating the circuit configuration of FIG. 9 K times.

In the subband decomposition adaptive FIR filter, the sparse subfilters are shown in Fig. 11 as an example of the frequency response according to the level after convergence. Where 1 is the frequency response of the 0th subfilter at the L (-1) level, 2 is the L (0) level, 3 is the L (1) level and 4 is the L Lt; / RTI > represents the frequency response of the subfilter in <

In FIG. 11, the regions indicated by (1) are desired responses selected as the passband of the interpolator, and the region (2) except (1) is an unwanted image due to a rare factor. Since the frequency response according to this level is directly connected to the band-pass characteristic (see FIG. 4) of the interpolator in wavelet transform, it has the transfer characteristic shown in FIG.

FIG. 12 shows an example in which a periodic noise canceller is constructed using the DWT-DSFS FIR adaptive filter of the present invention. Here, the signal S is a random pulse generated by a random signal generator and has a variable pulse width and an amplitude of 0.5. The periodic noise n ₀ is a sinusoidal wave with an amplitude of 0.5, and the period is defined as 12.8 samples and 2 samples.

In the simulation, the step size μ is 1 × 10 ^-5 , the equivalent order N of the adaptive filter is 128, and the conversion size M is 16.

Under such a condition, the signal S and the noise n ₀ are input simultaneously and noise cancellation is carried out to obtain a time domain and a DFT-USFS FIR adaptive filter for the square of the difference between the signal S and the system output signal S ₀ , And compared it with that used.

13A and 13B show convergence characteristics in the case where the noise period is 12.8 samples and 2 samples, respectively. From these results, it can be seen that convergence speeds when converted to Harr wavelet and D4 wavelet are similar when DWT-DSFS FIR adaptive filter is used. These convergence rates are 8 times faster than those using the time domain and DFT-USFS FIR adaptive filters.

FIG. 14 shows an example in which an inverse modeling (channel equalizer) is configured as another application example of the present invention.

The impulse response P _i in the channel equalizer is

The input signal S is white Gaussian (normal 0, variance 1), and the W value is 3.1 in Equation 16. The eigenvalue ratio of the M point wavelet transformed values is changed according to this value. The step size μ of the adaptive filter is 1 × 10 ^-4 , the equivalent order N is 32, the conversion size M is 8, and the delay line delay is 16.

The convergence characteristic at this time is shown in Fig. As can be seen from the above, the channel equalizer using the DWT-DSFS FIR adaptive filter according to the present invention has improved convergence speed by about 1.8 times as compared with the case using the DFT-USFS FIR adaptive filter, .

16 shows another example of the system identification (system identification) of the present invention. The condition here is that the signal S is white Gaussian (mean 0, variance 1), the system is a 32nd order lowpass impulse response, the step size μ of the adaptive filter is 1 × 10 ^-3 , the equivalent order N is 64, The conversion size M is 16, and the convergence characteristic of the system modeling at this time is shown in Fig.

As can be seen from this, it can be seen that the adaptive FIR filter of the present invention exhibits better convergence characteristics than the conventional adaptive FIR filter.

As described above, according to the present invention, wavelet transform is used as an interpolator in a subband decomposition adaptive FIR filter and a sub-band decomposition structure adaptation using a homogeneous sparse factor The convergence speed becomes faster than the FIR filter.

Claims (3)

A subband decomposition structure adaptive FIR filter comprising a wavelet transform and a subfilter having a diamond scarer factor according to a conversion level of the wavelet transform interpolator, Adaptive finite impulse response filter with generalized subband decomposition using subfilter with factor. 2. The method of claim 1, wherein the transfer function of the subfilter using the diamond scarring factor The (Where N is the order of the filter, M is the transform size, Is the wavelet transform level at which the k branches belong = -1, 0, 1, ... , J- 1), and J = And, k is the marker of (k = 0, 1, ... , M-1) of subbands, Is a rare factor (level It is different according to. However, = 0), Lt; RTI ID = 0.0 > k < ), And the output y (n) of the filter is (Where Is a weight vector composed of a coefficient matrix G of a sub-filter and / th coefficients of each sub-filter). The wavelet transform is a finite sub-band decomposition structure using a sub- Impulse response filter. The subfilter of claim 1 or 2, wherein the subfilter is a wavelet transformed input signal u ₀ (n), u ₁ (n), u ₂ (n), ... u ₇ (n) ,) Consists of eight filter elements ( (N) / E [U _K (n) ² ]}, and the coefficient value of the corresponding filter coefficient block is updated configuration, the first buffer memory blocks (4-1) a rough input signal _{(u 4 (n-2)} , u 5 (n-2), u 6 (n-2), u 7 (n-2)) The four filter elements of the second filter coefficient block 5-2 ) Outputs {2μ of the inputted computing unit 8 to the e (n) / E [U 4 (n) 2], 2μ e (n) / E [U 5 (n) 2], 2μ e (n) / E [U ₆ (n) ² ], ² μ e (n) / E [U ₇ (n) ² ]} to update the coefficient value of the corresponding filter coefficient block, 4-1) and a second buffer memory blocks (4-2) the coarse delay the input signal _{(u 2 (n-4)} , u 3 (n-4), u 4 (n-4), u 5 (n- 4), u ₆ (n-4), u ₇ (n-4) ) Is input to the output of the computing unit (8) {2μ e (n ) / E [U 2 (n) 2], 2μ e (n) / E [U 3 (n) 2], 2μ e (n) / E ^{_{[U 4 (n) 2]}} , 2μ e (n) / e [U 5 (n) 2], 2μ e (n) / e [U 6 (n) 2], 2μ e (n) / e [U ₇ (n) ² ]} to update the coefficient value of the corresponding filter coefficient block, and the first buffer memory block 4-1, the second buffer memory block 4-2, The delayed input signals u ₄ (n-6), u ₅ (n-6), u ₆ (n-6), u ₇ Four filter elements (5-4) (N) / E [U ₄ (n) ² ], 2 μe (n) / E [U ₅ (n) ² ] and 2 μe Is multiplied by [U ₆ (n) ² ], 2 μe (n) / E [U ₇ (n) ² ], and the coefficients of the corresponding filter coefficient block are updated. A finite impulse response filter of a generalized subband decomposition structure using a subfilter with a Dick sparse factor.