Design of optimal symmetric FIR receive filters

A method for designing optimal symmetric odd-length finite impulse response digital receive filters is proposed. The filter jointly minimises the mean power of intersymbol interference and additive noise or interference under the constraint that the filter coefficients are symmetric. The method yields exactly symmetric filters with the same performance as the earlier unconstrained design but with a lower computational complexity     

Zolotarev polynomials and optimal FIR filters

The algebraic form of Zolotarev polynomials refraining from their parametric representation is introduced. A recursive algorithm providing the coefficients for a Zolotarev polynomial of an arbitrary order is obtained from a linear differential equation developed for this purpose. The corresponding narrowband, notch, and complementary pair FIR filters are optimal in the Chebyshev sense. A recursion giving an explicit access to the impulse response coefficients is also presented. Some design examples are included to demonstrate the efficiency of the presented approach     

Design of optimal minimum phase FIR filters by direct factorization

An improved method of designing optimal minimum phase FIR filters by directly finding zeros is proposed. The zeros off the unit circle are found by an efficient special purpose root-finding algorithm without deflation. The proposed algorithm utilizes the passband minimum ripple frequencies to establish the initial points, and employs a modified Newton's iteration to find the accurate initial points for a standard Newton's iteration. We show, with examples, that the proposed algorithm can be used to design very long filters (L = 325) with very high stopband attenuations.     

Design of FIR filters with reduced computations

The performance of a symmetric nonrecursive filter can be improved by multiple use of the same filter. The method is based on an Amplitude Change Function (ACF). An approach to the design of nonrecursive filters using an ACF is discussed in this paper. The prototype filter chosen is a Recursive Running Sum (RRS) filter which does not require any multipliers for its implementation. The required filter specifications are met by multiple use of the RRS filters. The overall filter requires a much smaller number of multiplications and adders than the one designed using the conventional method. It is shown that this method provides reduced noise due to coefficient quantization and product quantization compared with the conventional design technique.     

Short-time Fourier analysis via optimal harmonic FIR filters

The Fourier coefficients (FCs) of quasiperiodic signals are assumed to be in random walk motion in order to represent a broader class. A state model for such quasiperiodic signals is derived. The optimal short-time estimate of the Fourier coefficients is obtained via the suggested optimal harmonic FIR filter (OHFF) based on this state-space signal model. The optimal harmonic FIR filter can be considered to be a generalization of the discrete Fourier transform (DFT) in the sense that it becomes the same as the DFT when the state model is for periodic signals and the filter length is equal to the order of the state model. The optimal harmonic FIR filter derived from the model, even with nonzero state noise and measurement noise, gives an exact harmonic estimate when an incoming signal is periodic and noiseless. It is shown by examples that the ability to suppress noise and the ability to resolve changes of the Fourier coefficients can be adjusted by the filter length and the noise covariance of the state model. Finally, the suggested scheme is compared with existing short-time Fourier analysis methods in a test signal that has time-varying Fourier coefficients     

Design of digital FIR notch filters

A new procedure for designing digital FIR notch filters for a specified notch frequency ω_d and 3-dB rejection bandwidth Δω has been proposed. Design formulae for computing the required weights and the length N for the filter have been derived. Illustrative examples confirming the new approach are also given     

Analytical design method for optimal equiripple comb FIR filters

A novel analytical design method for highly selective digital optimal equiripple comb finite-impulse response (FIR) filters is presented. The equiripple comb FIR filters are optimal in the Chebyshev sense. The number of notch bands, the width of the notch bands and the attenuation in the passbands can be independently specified. The degree formula and the differential equation for the generating polynomial of the filter is presented. Based on the differential equation, a fast simple algebraic recursive procedure for the evaluation of the impulse response of the filter is described. Its arithmetic robustness outperforms, by far, the known analytical design method. Highly selective equiripple comb FIR filters with thousands of coefficients can be designed. One example demonstrates the efficiency of the filter design.     

Design of FIR digital filters using tapped cascaded FIR Subfilters

This paper considers the design of an FIR digital filter by interconnecting a number of identical FIR subfilters with the aid of a few additional multipliers and adders. The overall structure is in the form of a tapped cascaded FIR subfilters. A composite method to determine the tapping coefficients along with the coefficients of the subfilter to approximate overall frequency response characteristic is proposed. Several numerical examples illustrating the proposed method are included.     

Analysis and optimal realization of pole-zero sensitivity for FIR digital filters

Aiming at the deviation of pole and zero in filters which caused by the finite word length (FWL) effects,the sensitivity of pole and zero for FIR digital filters to coefficient errors was studied based on the state-space model.Unlike the IIR filter,the system matrix in state-space model of the FIR filter was defective.A set of generalized eigenvectors of defective matrix was introduced to analyze the pole sensitivity and derive the measure expression,and optimal realizations with respect to pole-zero sensitivity for FIR filters were proposed by finding optimal transformation matrices according to the similarity transformation theory.Theoretical analysis and simulation experiments show that the poles of a FIR filter are more sensitive to coefficient errors,and the proposed optimal realizations can reduce the sensitivity.     

可规划相位FIR滤波器的神经网络设计方法

本文针对可规划相频响应的实系数FIR滤波器的逼近问题,采用一个三层复激活函数前馈神经网络来实现。该网络隐层各神经元的激活函数为复指数函数,将滤波器系数作为隐层各神经元到输出层的连接权值,通过对误差函数的最小化来调整权值,并根据网络特性与所要设计的滤波器的特点,提出了一些实际设计中训练样本集选取与误差加权值设置的规则。依托所采用的神经网络,根据上述规则,进行了两例可规划相频特性的实系数FIR滤波器的设计,结果表明所设计滤波器的相频响应较好地满足了设计要求。     

Design of FIR filters with extra constraints using modified LMSalgorithm

An adaptive approach to the design of linear phase low-pass FIR filters with extra constraints on filter coefficients is presented. In this approach, the procedures using the LMS adaptive algorithm are modified to include the constraints on the filter coefficients. Numerical examples are presented and compared to the results obtained using least-square design in the frequency domain in which the filter design problem is transformed into an equivalent nonlinear optimisation problem     

An iterative algorithm for optimal design of non-frequency-selective FIR digital filters

This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response （FIR） digital filters based on the windowing method. Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter, the key idea of the algorithm is minimizing the approximation error by successively modifying the design result through an iterative procedure under the condition of a fixed window length. In the iterative procedure, the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration. Because the approximation error can be specified variably, the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain. A design example is employed to illustrate the efficiency of the algorithm.     

Design of 3D optimal FIR filters for detecting linear trajectorysignal using object shape and velocity vector

A proposed design method for optimal FIR filters enhances moving objects with a specific velocity vector from other moving objects and noise. A stochastic process approach is applied to the problem using a priori information of signals and the probability distribution of velocity vectors     

Design of FIR filters for low implementation complexity

The minimisation of the total number of power-of-two terms is considered. The number of terms per coefficient is not constrained. Arbitrary phase filters are also designed where a method is introduced for the optimal utilisation of the filter gain. The method produces much better results than other methods in the literature with low computational requirements     

Design of linear-phase IIR filters from FIR specifications

A simple method is presented for the characterization of a stable IIR filter matching a finite portion of the impulse response and autocorrelation coefficients of a given FIR filter. It is shown that the problem is reduced to the solution of a set of linear equations derived using the impulse response and autocorrelation data. The method is characterized by its computational simplicity and is illustrated by some examples to show its superior performance when compared to the existing methods     

Design of FIR digital filters using prescribed subfilters

A method for the design of linear-phase digital filters by the tapped cascaded interconnection of identical subfilters is presented. The method is an extension of the method proposed by Saramaki (1987). An example is given to show that the number of distinct multipliers of the filter determined by the proposed method is less than that of filters determined by Saramaki's method (1987). We also consider the case in which the subfilters are determined by multiple use of a single filter. In particular, if we can make the subfilters multiplierless then the number or multiplications per sample required to implement the overall filter is less than that required by the direct-form minimax method. Methods for the design of computationally efficient filters are also developed based on the proposed transformation method. The multiplication rate of the overall filter is the same as that of the prototype filter. It is very low as compared to that designed by the equivalent direct-form minimax method. With the proposed transformation method, methods for the design of a filter having nth-order tangency at both ends (0, π) are also developed. This is an extension of Vaidynathan's method (1985) and the proposed transformation method. The advantages of the method are that the resulting filters have very flat passbands and the stopbands are computationally efficient.     

A design algorithm for optimal low-pass nonlinear phase FIR digital filters

The transfer function of the low-pass nonlinear phase finite impulse response (NLPFIR) digital filter is decomposed into a nonlinear phase part and a linear phase part. An algorithm is proposed to iteratively design the magnitude of the linear phase part and the squared magnitude of the nonlinear phase part by directly calling the Remez algorithm of McClellan, et al. [1]. In the design of the nonlinear phase part, we assume that the linearity constraint on the phase is dropped but the phase response is not specified. A scheme is incorporated into our algorithm so that it can design the filter with the desired ripple ratio. This approach also leads to a method for finding the minimum ripple ratio for the given orders of the two parts and band edges of the filters. The filters with ripple ratio larger than this minimum value can be designed by our algorithm and neither passband nor stopband ripples are required to be prescribed. Analysis of roundoff noise reveals that the cascade filter implementation usually needs higher wordlengths than its direct for counterpart for the same roundoff noise performance.     

B-spline FIR filters

This paper presents an efficient procedure for the design of interpolated FIR (IFIR) filters with linear phase. The algorithm uses the uniform B-spline function as an interpolator and solves the optimal Chebyshev approximation problem on the optimal subinterval. The technique can be used for the design of general lowpass, highpass and bandpass filters. While the number of multiplications of the IFIR filter is dependent on the bandwidth and the center frequency of the desired filter, it provides the minimum number of multiplications achievable and nearly always provides a substantial reduction when compared to Parks-McClellan designs.     

FIR filters with field-programmable gate arrays

Distributed arithmetic techniques are the key to efficient implementation of DSP algorithms in FPGAs. The distributed arithmetic process is briefly described. A representative DSP design application in the form of an 8 tap FIR filter is offered for the Xilinx XC3042 field programmable logic array (FPGA). The design is presented in sufficient detail—from filter specifications via filter design software through detailed logic of salient data and control functions to obtain a realistic placing and routing of configurable logic block (CLBs) and in/out block (IOBs) components for simulation verification and performance evaluation vis-a-vis commercially available dedicated 8 tap FIR filter chips.     

最优噪声整形滤波器的设计

在需要对信号进行再量化的场合,可以通过加入dither来避免小信号再量化所产生的谐波失真,但同时会使噪声功率增加。这种情况下,可以利用人耳的心理声学特性,通过噪声整形来降低噪声的可闻性,提高实际的信噪比,改善音质。本文提出了两种新的设计最优噪声整形滤波器的方法-遗传算法和非线性优化算法,并分别实现了原采样率下和过采样率下基于心理声学模型的最优噪声整形滤波的设计。结果证明,该方法灵活方便、实现效果良好。