Design of linear phase FIR filters with a maximally flat passband (original) (raw)
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Digital Signal Processing is one of the most powerful technologies that are shaping science and engineering in the twenty-first century. Revolutionary changes have already been made in a broad range of fields: communications, medical imaging, radar and sonar, and high fidelity music reproduction, to name just a few. Each of these areas has developed a comprehensive DSP technology, with its own algorithms, mathematics, and specialized techniques. The digital filters are an essential part of DSP. In fact, their extraordinary performance is one of the key reasons that DSP has become so popular. The purpose of the filters is to allow some frequencies to pass unaltered, while completely blocking others. The digital filters are mainly used for two purposes: separation of signals that have been combined, and restoration of signals that have been distorted in some way.
A computer program for designing optimum FIR linear phase digital filters
IEEE Transactions on Audio and Electroacoustics, 1973
This paper presents a general-purpose computer program which is capable of designing a large class of optimum (in the minimax sense) FIR linear phase digital filters. The program has options for designing such standard filters as lowpass, high-pass, bandpass, and bandstop filters, as well as multipassband-stopband filters, differentiators, and Hilbert transformers. The program can also be used to design filters which approximate arbitrary frequency specifications which are provided by the user. The program is written in Fortran, and is carefully documented both by comments and by detailed flowcharts. The filter design algorithm is shown to be exceedingly efficient, e.g., it is capable of designing a filter with a 100-point impulse response in about 20 s.
A nearly optimum linear-phase digital FIR filters design
Digital Signal Processing, 2011
A new simple method to design linear-phase finite impulse response (FIR) digital filters, based on the steepest-descent optimization method, is presented in this paper. Starting from the specifications of the desired frequency response and a maximum approximation error a nearly optimum digital filter is obtained. Tests have shown that this method is alternative to other traditional ones such as Frequency Sampling and Parks–McClellan, mainly when other than brick wall frequency response is required as a desired frequency response.
Computación y Sistemas
An alternative method for the design of type I Halfband FIR filters with flat magnitude and narrow transition bands is presented. The methodology shown is based on the derivation of a quadratic programming problem with inequality constraints, which represents a set of linear equations obtained from flat and ripple restrictions imposed over the frequency response of the filter. The design is based on maximally flat constraints. The obtained filters have narrow transition bands as compared to those presented in other maximally flat based designs. The proposed method is not ripple free as it does not take into account all the maximally flat restrictions. Then, control of side lobes and transition band is performed using a weighting matrix and inequality constraints as side lobes bounds. The design of type IV FIR digital differentiators through the proposed method is also shown. Examples of design, which compare the proposed method with others presented in the literature, are provided to verify the effectiveness of the proposed method.
An Based Method for the Design of 1-D Zero Phase FIR Digital Filters
1997
Finite impulse response (FIR) filters obtained with the classical L 2 method have performance that is very sensitive to the form of the ideal response selected for the transition region. It is known that design requirements do not constraint in any way the ideal response inside this region. Most existing techniques utilize this flexibility. By selecting various classes of functions to describe the undefined part of the ideal response they develop methods that improve the performance of the L2 based filters. In this paper we propose a means for selecting the unknown part of the ideal response optimally. Specifically by using a well-known property of the Fourier approximation theory we introduce a suitable quality measure. The proposed measure is a functional of the ideal response and depends on its actual form inside the transition region. Using variational techniques we succeed in minimizing the introduced criterion with respect to the ideal response and thus obtain its corresponding optimum form. The complete solution to the problem can be obtained by solving a simple system of linear equations suggesting a reduced complexity for the proposed method. An extensive number of design examples show the definite superiority of our method over most existing non min-max design techniques, while the method compares very favorably with min-max optimum methods. Finally we prove that the approximation error function of our filter has the right number of alternating extrema, required by the L 1 criterion, in the passband and stopband. This results in a significant convergence speed up, if our optimum solution is used as an initialization scheme, of the Remez exchange algorithm.
Signal Processing
This paper deals with the design of variable-bandwidth linear-phase FIR digital filters. Such filters are implemented as a linear combination of fixed-coefficient linear-phase filters and the variable bandwidth characteristics are provided by a tuning parameter embedded in the filter structure. These filters are designed in a least-square sense by formulating an error function reflecting the difference between the desired variable bandwidth filter and the practical filter represented as a linear combination of fixed-coefficient filters in a quadratic form. The filter coefficients are obtained by solving a system of linear equations comprising of a block-symmetric positive-definite matrix in which each block is a Toeplitz-plus-Hankel matrix. Consequently, a significant reduction in computational complexity can be achieved in obtaining the entries of this matrix. Moreover, closed-form expressions are provided for both the block-symmetric matrix as well as the vector involved in the system of linear equations.
Minimax design of two-dimensional FIR digital filters by using an interior-point algorithm
1993 IEEE International Symposium on Circuits and Systems
This paper considers the design of two dimensional (2-D) linear phase FIR digital filters optimal in the minimax sense. A design method based on an &ne-scaling variant of Karmarkar's linear programming algorithm is presented. In the design process, we first formulate the design problem into a linear programming form. To avoid the huge computation load and storage space required by using a standard simplex algorithm, we present a Karmarkar's algorithm based method to solve the design problem. In each iteration of the proposed method, we only need to calculate a weighted least square (WLS) solution. Nearly optimal solutions can be obtained after several iterations. Design examples and comparison are presented to show the effectiveness of the proposed method.
Design of linear-phase FIR filters with minimum Hamming distance
Proc. IEEE Nordic Signal Processing …, 2002
In this paper a new approach for the design of linear phase FIR filters with discrete coefficients is proposed. A mixed integer linear programming (MILP) problem is formulated that minimizes the total Hamming distance between the adjacent coefficients, i.e., the number of bit switches of the coefficients. The Hamming distance between the coefficients is a good measure of the power consumption, when the FIR filters is implemented on a programmable architecture. The method is applicable both for filters with a specified passband gain and filters where the normalized peak ripple magnitude is of interest. In both cases the globally minimal solution is found subject to the filter specification, filter order, and number of coefficient bits. A preprocessing method that removes a significant part of the variables is also proposed and it is shown by an example that this method speeds up the optimization process significantly. Both two's complement and signed magnitude representation of the coefficients are considered.
Design and characterization of optimal FIR filters with arbitrary phase
IEEE Transactions on Signal Processing, 1993
We present a new algorithm for designing a Chebyshev optimal FIR filter that approximates an arbitrary complex-valued frequency response. This algorithm computes the optimal filter by solving the dual to the filter design problem. It is guaranteed to converge theoretically and requires O ( N 2 ) computations per iteration for a filter of length N . For the first time, properties of the optimal filter are derived, and the case where the desired filter has arbitrary constant group delay is studied in detail.
An L2-based method for the design of 1-D zero phase FIR digital filters
IEEE Transactions on Circuits and Systems I-regular Papers, 1997
Finite impulse response (FIR) filters obtained with the classical L 2 method have performance that is very sensitive to the form of the ideal response selected for the transition region. It is known that design requirements do not constraint in any way the ideal response inside this region. Most existing techniques utilize this flexibility. By selecting various classes of functions to describe the undefined part of the ideal response they develop methods that improve the performance of the L2 based filters. In this paper we propose a means for selecting the unknown part of the ideal response optimally. Specifically by using a well-known property of the Fourier approximation theory we introduce a suitable quality measure. The proposed measure is a functional of the ideal response and depends on its actual form inside the transition region. Using variational techniques we succeed in minimizing the introduced criterion with respect to the ideal response and thus obtain its corresponding optimum form. The complete solution to the problem can be obtained by solving a simple system of linear equations suggesting a reduced complexity for the proposed method. An extensive number of design examples show the definite superiority of our method over most existing non min-max design techniques, while the method compares very favorably with min-max optimum methods. Finally we prove that the approximation error function of our filter has the right number of alternating extrema, required by the L 1 criterion, in the passband and stopband. This results in a significant convergence speed up, if our optimum solution is used as an initialization scheme, of the Remez exchange algorithm.