阅读说明：本技术 一种farrow滤波器的系数拟合方法 (Coefficient fitting method of FARROW filter ) 是由 李非 肖琨 于 2019-09-17 设计创作，主要内容包括：本发明公开了一种基于小波函数拟合的FARROW滤波器系数拟合方法,首先,对低通滤波器进行多相分解得到多相滤波器系数矩阵；接着,对该系数矩阵的每一列系数进行小波拟合,通过最小二乘法计算得到小波拟合系数；最后,将拟合得到的系数加载到FARROW滤波器结构中,输入信号通过该结构即可输出期望位置处的重采样输出值。本发明能够降低滤波器系数拟合时出现的震荡现象,与传统多项式拟合相比在相同拟合阶数情况下,改变尺度因子可以有效的提高拟合精度,提高通用解调器的计算效率。(The invention discloses a FARROW filter coefficient fitting method based on wavelet function fitting, which comprises the following steps of firstly, carrying out multi-phase decomposition on a low-pass filter to obtain a multi-phase filter coefficient matrix; then, performing wavelet fitting on each column of coefficients of the coefficient matrix, and calculating by a least square method to obtain a wavelet fitting coefficient; and finally, loading the coefficient obtained by fitting into a FARROW filter structure, and outputting a resampling output value at the expected position by the input signal through the structure. The invention can reduce the oscillation phenomenon generated during the fitting of the filter coefficient, and compared with the traditional polynomial fitting, under the condition of the same fitting order, the fitting precision can be effectively improved by changing the scale factor, and the calculation efficiency of the general demodulator is improved.)

1. a method of coefficient fitting of a FARROW filter, the method comprising:

(1) carrying out polyphase decomposition on the low-pass filter to obtain a polyphase filter coefficient matrix:

for a FIR filter with KI tap coefficients, the tap coefficients are represented in the form of I rows and K columns:

wherein I is 0,1, …, I-1;

(2) performing wavelet fitting on each column of coefficients of the FIR filter coefficient matrix to obtain wavelet fitting coefficients:

setting fitting function

The necessary condition for obtaining the extreme value isWherein s is 0,1, …, U; solving through the formula to obtain a wavelet fitting coefficient a_0,k、a_1,k、…、a_U,k；

(3) Loading the fitted coefficient into a FARROW filter structure, and outputting a resampling output value at a desired position by an input signal through the structure:

when t is nT_x+ΔT_xWhen Δ is 0. ltoreq. Δ.ltoreq.1, byObtaining the coefficient of the polyphase sub-filter; at nT_x+ΔT_xThe output at that moment is:

Technical Field

The invention relates to the technical field of digital signal processing, in particular to a coefficient fitting method of a FARROW filter.

Background

The general demodulator adapting to different modulation and code rates meets the requirements of future communication technology development, and sampling rate conversion is one of key technologies for realizing the general demodulator. For signals of different modulation and code rate, the symbol rate is also varied, and in order to improve the accuracy of the timing error estimation and the carrier frequency offset estimation, the equivalent sampling rate of the input signal is usually required to be an integer multiple of the symbol rate, so the equivalent sampling rate of the signal must be processed before such estimation of the signal.

In order to improve the computational efficiency of the system and reduce the consumption of resources, the sampling rate conversion of the general demodulator is mainly realized by using a polyphase filtering structure, including using polynomial piecewise fitting filter coefficients. The polynomial piecewise fitting has the defects that when the number of fitting points is large, the polynomial degree is high, and oscillation is easy to generate, so that the fitting precision is influenced.

Disclosure of Invention

The invention provides a wavelet function fitting-based FARROW filter coefficient fitting method, which aims to reduce the oscillation phenomenon generated during filter coefficient fitting.

The technical scheme of the invention is as follows: firstly, carrying out polyphase decomposition on a low-pass filter to obtain a polyphase filter coefficient matrix; then, performing wavelet fitting on each column of coefficients of the coefficient matrix, and calculating by a least square method to obtain a wavelet fitting coefficient; and finally, loading the coefficient obtained by fitting into a FARROW filter structure, and outputting a resampling output value at the expected position by the input signal through the structure.

The detailed technical scheme is as follows:

(1) carrying out polyphase decomposition on the low-pass filter to obtain a polyphase filter coefficient matrix:

for a FIR filter with KI tap coefficients, the tap coefficients are represented in the form of I rows and K columns:

h(0) h(I) ... h((K-1)I)

h(1) h(I+1) ... h((K-1)I+1)

... ... ... ...

h(i) h(I+i) ... h((K-1)I+i)；

h(i+1) h(I+i+1) ... h((K-1)I+i+1)

... ... ...

h(I-1) h(2I-1) ... h(KI-1)

wherein I is 0,1, …, I-1.

(2) Performing wavelet fitting on each column of coefficients of the FIR filter coefficient matrix to obtain wavelet fitting coefficients:

setting fitting function

To satisfy the condition of tolerance

The scale coefficient d belongs to Z, s is a displacement coefficient, U is a fitting order, and a is_s,kTo fit coefficients to the kth column, for any K, K is 0,1, …, K-1, the expression is defined:

wherein the weight coefficient δ_i＞0，U≤I；

The necessary condition for obtaining the extreme value is

Wherein s is 0,1, …, U; solving through the formula to obtain a wavelet fitting coefficient a_0,k、a_1,k、…、a_U,k。

(3) Loading the fitted coefficient into a FARROW filter structure, and outputting a resampling output value at a desired position by an input signal through the structure:

when t is nT_x+ΔT_xWhen Δ is 0. ltoreq. Δ.ltoreq.1, by

Obtaining the coefficient of the polyphase sub-filter; at nT_x+ΔT_xThe output at that moment is:

Detailed Description

The problem of sampling rate conversion can be summarized as a resampling process, first sampling the signal x (nT)_x) Reconstruction into an analog signal:wherein T is_xIs the sampling period, at t ═ mT_yResampling y (t) yields:

the process of interpolating the signal is the process of sampling rate conversion, which is commonThe interpolation method is integral multiple interpolation, i.e. I-1 zero values are inserted between two original sampling points, and I is an interpolation factor; however, in practice, the symbol timing is independent of the sampling clock, and therefore the sampling factor is not an integer multiple. Impulse response of ideal interpolation filterBecause the interpolation filter is non-causal and can only approach the ideal characteristic infinitely, in order to improve the calculation efficiency and save the hardware resource, the invention adopts the polyphase filter structure to realize the coefficient fitting of the FARROW filter.