CN113676156B - LMS-based arbitrary amplitude-frequency response FIR filter design method - Google Patents
LMS-based arbitrary amplitude-frequency response FIR filter design method Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 24
- 238000013461 design Methods 0.000 title claims abstract description 17
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 14
- 239000013598 vector Substances 0.000 claims description 18
- 238000005070 sampling Methods 0.000 claims description 4
- 238000004364 calculation method Methods 0.000 claims description 3
- 238000006243 chemical reaction Methods 0.000 claims description 3
- 238000001228 spectrum Methods 0.000 claims 1
- 238000001914 filtration Methods 0.000 description 6
- 230000003044 adaptive effect Effects 0.000 description 4
- 238000010586 diagram Methods 0.000 description 2
- 238000005259 measurement Methods 0.000 description 2
- 241000191291 Abies alba Species 0.000 description 1
- 238000009825 accumulation Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
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- 238000010183 spectrum analysis Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
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Classifications
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H21/00—Adaptive networks
- H03H21/0012—Digital adaptive filters
- H03H21/0043—Adaptive algorithms
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H2017/0072—Theoretical filter design
- H03H2017/0081—Theoretical filter design of FIR filters
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H21/00—Adaptive networks
- H03H21/0012—Digital adaptive filters
- H03H21/0043—Adaptive algorithms
- H03H2021/0056—Non-recursive least squares algorithm [LMS]
Abstract
The invention provides a design method of an arbitrary amplitude-frequency response FIR filter based on LMS, wherein the FIR filter is determined to be a linear phase FIR filter, and the method comprises the following steps: determining the coefficient length of a filter to be odd or even, and selecting different FIR filter amplitude-frequency response formulas according to the coefficient length; determining an iteration model of the LMS algorithm according to the determined coefficient length of the filter; discretizing frequency points in a filter frequency band, and determining a sequence of frequency points and amplitude pairs in an amplitude-frequency curve; iterating once for the input value of each frequency point until the iterative function converges. The design method provided by the invention is simple to realize, fast in speed and easy to realize in engineering, can be used for designing a band-pass filter and a low-pass filter, has a linear phase, and compensates the unevenness error of the channel on the basis of not influencing the phase information of the signal so as to improve the signal quality.
Description
Technical Field
The invention belongs to the technical field of filter design, and particularly relates to an arbitrary amplitude-frequency response FIR filter design method based on LMS.
Background
Amplitude flatness and phase linearity are important factors affecting the performance improvement of the receiver, and for the receiving system, the spectrum analysis function is the most basic and widely used function, and the amplitude flatness in the passband affects the amplitude measurement accuracy. When the receiver system design is completed, it is a necessary and critical step to design a compensation filter to control the in-band flatness of the receiver channels to within the required tolerance range given the channel amplitude-frequency curve.
The common FIR filter design method comprises a window function method, an optimal approximation method, an equal ripple approximation method and the like, and only in-band amplitude flatness is required in the conventional design requirement. The amplitude-frequency characteristics of the hardware system are often not flat, so the in-band amplitude of the filter to be designed is arbitrary. The current design method (such as an optimal approximation method and an equal ripple approximation method) has high algorithm complexity and large engineering application difficulty, and is not suitable for the current scene.
Adaptive filtering is an important content of modern signal processing, solving how to adaptively update the filter coefficients to filter out the wanted signal. The least mean square algorithm (LMS algorithm for short) is one of the adaptive filtering methods, and is based on wiener filtering, and then the filter coefficients are iteratively updated by means of development of the steepest descent algorithm, so that the error between the output signal of the filter and the expected signal is infinitely reduced. A block diagram of a conventional LMS adaptive filtering system implementation is shown in fig. 1.
Disclosure of Invention
In order to solve the technical problems, the invention provides a design method of an arbitrary amplitude-frequency response FIR filter based on LMS, wherein the FIR filter is determined to be a linear phase FIR filter, and the method comprises the following steps:
step 1, determining that the coefficient length of a filter is odd or even, and selecting different FIR filter amplitude-frequency response formulas according to the coefficient length; turning to step 2;
step 2, determining an iteration model of the LMS algorithm according to the determined coefficient length of the filter; turning to step 3;
step 3, discretizing frequency points in the frequency band of the filter, and determining a sequence of frequency points and amplitude pairs in an amplitude-frequency curve;
(f 0 ，A 0 )，(f 1 ，A 1 )，(f 2 ，A 2 )，……，(f M-1 ，A M-1 )
wherein f i Is the frequency, A i Is the corresponding amplitude; turning to step 4;
and 4, iterating once aiming at the input value of each frequency point until the iterated function converges.
Preferably, when the coefficient length of the filter is odd, the amplitude-frequency response formula of the FIR filter:
wherein, |·| refers to taking a complex modulus value, which characterizes the power gain value of the current FIR filter for the spectral component at the frequency point ω. Coefficient a n And filter coefficient b n The conversion relation of (2) is as follows:
wherein: omega is a frequency point, and N is more than or equal to 1 and less than or equal to N.
Preferably, when the filter coefficient length N is even, the FIR filter amplitude-frequency response formula:
coefficient alpha n And filter coefficient b n The relationship of (2) is as follows:
wherein: omega is a frequency point, and N is more than or equal to 1 and less than or equal to N.
Preferably, the discretizing of the frequency points in the filter frequency band includes: discretizing the frequency point omega to obtain:
ω k ＝2πf k ，0≤k≤M-1，
wherein f k And M is the number of frequency points corresponding to the amplitude-frequency response curve to be fitted for the frequency value normalized relative to the sampling rate.
Further, the input signal for each iteration is a vector:
and the weight vector is initialized to a 0-column vector, where T represents the transpose of the vector.
Further, each time the iterative calculation is performed, the weight vector w (i) is updated:
W(k+1)＝w(k)+μ·x(k)·е * (k)
wherein the method comprises the steps of * Conjugate of finger and complex number
Desired signal d (i) estimate:
d(k+1)＝w H (k+1)·x(k+1)
where H refers to the conjugate transpose of the vector. Estimation error e (i):
e(k+1)＝D(k+1)-d(k+1)
obtaining a weight coefficient alpha:
α＝w *
wherein w is * Is the weight coefficient of the update that is to be applied, * refers to complex conjugate; d (i) means A 0 …A M-1 And (5) constructing a vector.
The method provided by the invention is simple to realize, high in speed and easy to realize engineering, can be used for designing a band-pass filter and a low-pass filter, has a linear phase, and compensates the uneven errors of the channel on the basis of not influencing the phase information of the signal so as to improve the signal quality.
Drawings
FIG. 1 is a block diagram of LMS transversal adaptive filtering;
FIG. 2 is an iterative error curve;
FIG. 3a filter amplitude-frequency response;
fig. 3b compensates the front-to-back amplitude frequency curve.
Detailed Description
The conventional LMS algorithm performs self-adaptive filtering on signals, the invention combines the design of any amplitude-frequency response filter with the LMS algorithm, and the stable filter coefficient is iterated by utilizing the LMS self-adaptive theory.
Unlike the conventional LMS algorithm flow, the input signal is not some stationary random signal, but rather a frequency factor in the filter transfer function, and the desired signal is the required filter amplitude-frequency response. Because of limited frequency factors, namely limited algorithm input length, the invention adopts a loop iteration method to finally obtain stable filter coefficients, so that the amplitude-frequency response of the filter coefficients is infinitely close to the expected amplitude-frequency response.
The design method provided by the invention is simple to realize, fast in speed and easy to realize in engineering, can be used for designing a band-pass filter and a low-pass filter, has a linear phase, and compensates the unevenness error of the channel on the basis of not influencing the phase information of the signal so as to improve the signal quality.
The following detailed description of specific embodiments of the invention refers to the accompanying drawings.
A. Channel model
For a receiving system, it can be considered a Linear Time Invariant (LTI) system, and the response of the system to any input signal can be expressed in the form of a unit impulse response. Linear time-invariant systems can be divided into two types: a system with a finite long impulse response (FIR) and a system with an Infinite Impulse Response (IIR).
The receiver is regarded as an FIR system, the amplitude-frequency response of the filter to be compensated is obtained according to the amplitude-frequency response of the system obtained by measurement, and the FIR filter is designed to obtain the coefficient of the FIR filter.
The system function of the FIR filter of length N is:
wherein b n For the filter coefficients to be calculated.
Since the present invention performs filter design only for amplitude-frequency response and does not involve phase-frequency response, the FIR filter to be designed is set as a FIR filter of linear phase. At this time, the FIR filter compensates the amplitude-frequency response of the system channel, and the phase information is unchanged, so that only the in-band signal is subjected to the same delay.
Since the impulse response of the linear phase FIR filter is symmetrical or antisymmetric, the invention uses the filter coefficient pair as an example, and can be obtained in the same way under the antisymmetric condition.
(1) The filter coefficient length N is odd
The FIR filter amplitude-frequency response formula:
coefficient a n And filter coefficient b n The relationship of (2) is as follows:
(2) The filter coefficient length N is even
The FIR filter amplitude-frequency response formula:
coefficient a n And filter coefficient b n The relationship of (2) is as follows:
B. principle of algorithm
According to the formula of the linear phase FIR filter in A, the amplitude-frequency response of the filter is obtained as a sine function by coefficient weighted accumulation, so that under the requirement of the amplitude-frequency response of the current filter, the algorithmThe coefficient a needs to be obtained n Further obtaining a filter coefficient b according to a conversion formula n 。
Taking N as an odd number as an example to deduce an iteration model under the LMS algorithm.
Discretizing the frequency point omega to obtain:
ω k ＝2πf k ，0≤k≤M-1，
wherein f k And M is the number of frequency points corresponding to the amplitude-frequency response curve to be fitted for the frequency value normalized relative to the sampling rate.
Because the amplitude-frequency response of the linear phase FIR filter is symmetrical relative to zero frequency, the amplitude-frequency curve to be fitted can be inBetween them. The amplitude frequency curve frequency point/amplitude pair sequence is assumed as follows:
(f 0 ，A 0 )，(f 1 ，A 1 )，(f 2 ，A 2 )，……，(f M-1 ，A M-1 )
FIR filter LMS iterative model:
(1) The iteration mode is as follows: the iteration is performed once for the input value of each frequency point until convergence.
(2) The input signal for each iteration is:
(3) The weight vector is initialized to a 0 column vector.
The iterative process:
and (5) updating weight vectors:
W(k+1)＝w(k)+μ·x(k)·е * (k)
estimating a desired signal:
d(k+1)＝w H (k+1)·x(k+1)
estimation error e (i):
e(k+1)＝D(k+1)-d(k+1)
obtaining a weight coefficient alpha:
α＝w *
C. simulation of
The algorithm iteration error curve of the 128-order FIR filter is shown in FIG. 2 at a 100MHz sampling rate, a 20MHz bandwidth, and a 25MHz center frequency and 40 loop iterations.
From fig. 3 (a), it can be seen that the amplitude-frequency response of the designed filter is basically close to the required amplitude-frequency curve, and after calculation and compensation, the amplitude-frequency curve fluctuation obtained by statistics in fig. 3 (b) is reduced from 2.9dB to 0.124dB, so that the in-band flatness of the system is greatly improved.
Finally, it should be noted that the above-mentioned embodiments are merely for illustrating the technical solution of the embodiment of the present invention, and not for limiting, and although the embodiment of the present invention has been described in detail with reference to the above-mentioned preferred embodiments, it should be understood by those skilled in the art that modifications and equivalent substitutions can be made to the technical solution of the embodiment of the present invention without departing from the spirit and scope of the technical solution of the embodiment of the present invention.
Claims (3)
1. A method for designing an LMS-based arbitrary amplitude-frequency response FIR filter, wherein the FIR filter is determined as a linear-phase FIR filter, the method comprising the steps of:
step 1, determining that the coefficient length of a filter is odd or even, and selecting different FIR filter amplitude-frequency response formulas according to the coefficient length; turning to step 2;
step 2, determining an iteration model of the LMS algorithm according to the determined coefficient length of the filter; turning to step 3:
step 3, discretizing frequency points in the frequency band of the filter, and determining a sequence of frequency points and amplitude pairs in an amplitude-frequency curve;
(f 0 ，A 0 )，(f 1 ，A 1 )，(f 2 ，A 2 )，……，(f M-1 ，A M-1 )
wherein f i Is the frequency, A i Is the corresponding amplitude; turning to step 4;
the discretizing of the frequency points in the filter frequency band comprises the following steps: discretizing the frequency point omega to obtain:
ω k ＝2πf k ，0≤k≤M-1，
wherein f k The frequency value normalized relative to the sampling rate is M, which is the number of frequency points corresponding to the amplitude-frequency response curve to be fitted;
step 4, iterating once aiming at the input value of each frequency point until the iterated function converges; the input signal for each iteration is the vector:
and the weight vector is initialized to a 0-column vector, where T represents the transpose of the vector;
at each iterative calculation, the weight vector w (i) is updated:
w(k+1)＝w(k)+μ·x(k)·e * (k)
desired signal d (i) estimate:
d(k+1)＝w H (k+1)·x(k+1)
wherein H refers to the conjugate transpose of the vector, the estimation error e (i):
e(k+1)＝D(k+1)-d(k+1)
obtaining a weight coefficient alpha:
α＝w *
wherein w (k) is the kth weight vector, the kth error e (k), the kth desired signal D (k), the kth input signal x (k), D (i) means A 0 …A M-1 Vectors of constitution, w * The updated weight coefficients refer to complex conjugates.
2. The design method of claim 1, wherein when the coefficient length of the filter is odd, the FIR filter amplitude-frequency response formula:
wherein, I and I refer to complex modulus values, which represent the power gain values of the current FIR filter to the frequency spectrum components at the frequency point omega; coefficient alpha n And filter coefficient b n The conversion relation of (2) is as follows:
wherein: omega is the frequency bin.
3. The design method of claim 1, wherein when the filter coefficient length N is even, the FIR filter amplitude-frequency response formula:
coefficient alpha n And filter coefficient b n The relationship of (2) is as follows:
wherein: omega is a frequency point, and N is more than or equal to 1 and less than or equal to N/2.
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Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5282155A (en) * | 1992-11-19 | 1994-01-25 | Bell Communications Resarch, Inc. | Adaptive digital filter architecture for parallel output/update computations |
| JPH10242737A (en) * | 1997-02-27 | 1998-09-11 | Atr Kankyo Tekiou Tsushin Kenkyusho:Kk | Fir type digital filter and its coefficient arithmetic unit, digital beam forming device and adaptive digital beam forming device |
| TW465196B (en) * | 1999-02-26 | 2001-11-21 | Texas Instruments Inc | Phase-shift calculation method, and system implementing it, for a finite-impulse-response (FIR) filter |
| US6618740B1 (en) * | 1998-12-31 | 2003-09-09 | Texas Instruments Incorporated | Method and architecture for controlling asymmetry of an LMS adaptation algorithm that controls FIR filter coefficients |
| CN101295969A (en) * | 2008-06-26 | 2008-10-29 | 湖南大学 | Design method of high-order limited impulse response digital filter |
| CN102132491A (en) * | 2008-08-25 | 2011-07-20 | 杜比实验室特许公司 | Method for determining updated filter coefficients of an adaptive filter adapted by an lms algorithm with pre-whitening |
| CN102195616A (en) * | 2010-03-02 | 2011-09-21 | 哈曼贝克自动系统股份有限公司 | Efficient sub-band adaptive FIT-filtering |
| CN111903233B (en) * | 2008-10-22 | 2014-06-11 | 中国电子科技集团公司第五十四研究所 | Broadband beam forming method based on specific group delay finite impulse response filter |
| CN105680825A (en) * | 2016-02-16 | 2016-06-15 | 天津大学 | Digital filter analytical design method and filter thereof |
| CN107576323A (en) * | 2017-08-21 | 2018-01-12 | 陕西华燕航空仪表有限公司 | Based on the combined optical fibre gyro filtering method of FIR and LMS adaptive-filterings |
| WO2019170020A1 (en) * | 2018-03-09 | 2019-09-12 | 电信科学技术研究院有限公司 | Method and device for updating finite impulse response filter coefficient vector |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE10210234B4 (en) * | 2002-03-08 | 2011-02-03 | Advanced Micro Devices, Inc., Sunnyvale | LMS-based channel estimation |
| WO2005045829A1 (en) * | 2003-11-11 | 2005-05-19 | Matsushita Electric Industrial Co., Ltd. | Filter coefficient adjusting circuit |
-
2021
- 2021-08-09 CN CN202110918349.3A patent/CN113676156B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5282155A (en) * | 1992-11-19 | 1994-01-25 | Bell Communications Resarch, Inc. | Adaptive digital filter architecture for parallel output/update computations |
| JPH10242737A (en) * | 1997-02-27 | 1998-09-11 | Atr Kankyo Tekiou Tsushin Kenkyusho:Kk | Fir type digital filter and its coefficient arithmetic unit, digital beam forming device and adaptive digital beam forming device |
| US6618740B1 (en) * | 1998-12-31 | 2003-09-09 | Texas Instruments Incorporated | Method and architecture for controlling asymmetry of an LMS adaptation algorithm that controls FIR filter coefficients |
| TW465196B (en) * | 1999-02-26 | 2001-11-21 | Texas Instruments Inc | Phase-shift calculation method, and system implementing it, for a finite-impulse-response (FIR) filter |
| CN101295969A (en) * | 2008-06-26 | 2008-10-29 | 湖南大学 | Design method of high-order limited impulse response digital filter |
| CN102132491A (en) * | 2008-08-25 | 2011-07-20 | 杜比实验室特许公司 | Method for determining updated filter coefficients of an adaptive filter adapted by an lms algorithm with pre-whitening |
| CN111903233B (en) * | 2008-10-22 | 2014-06-11 | 中国电子科技集团公司第五十四研究所 | Broadband beam forming method based on specific group delay finite impulse response filter |
| CN102195616A (en) * | 2010-03-02 | 2011-09-21 | 哈曼贝克自动系统股份有限公司 | Efficient sub-band adaptive FIT-filtering |
| CN105680825A (en) * | 2016-02-16 | 2016-06-15 | 天津大学 | Digital filter analytical design method and filter thereof |
| CN107576323A (en) * | 2017-08-21 | 2018-01-12 | 陕西华燕航空仪表有限公司 | Based on the combined optical fibre gyro filtering method of FIR and LMS adaptive-filterings |
| WO2019170020A1 (en) * | 2018-03-09 | 2019-09-12 | 电信科学技术研究院有限公司 | Method and device for updating finite impulse response filter coefficient vector |
Non-Patent Citations (2)
| Title |
|---|
| Design of Linear Phase FIR Filters Using the LMS Algorithm;Sumit Roy;《IEEE TRANSACTIONS ON SIGNAL PROCESSING》;第41卷(第4期);1685-1689 * |
| 基于LMS算法的自适应次声滤波器设计;王谦;《中国优秀硕士学位论文全文数据库信息科技辑》(第05（2010）期);I135-146 * |
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