Parks–McClellan filter design algorithm

Abstract: This paper discusses the design of two-dimensional (2-D) linear-phase FIR digital filters by transformations of one-demensional (l-D) filters, using a technique first presented by McClellan. His original transformations are generalized and several algorithms are presented for the design of the generalized transformations. Examples are included to demonstrate, the versatility of the design method.

Abstract: The application of a general-purpose integer-programming computer program to the design of optimal finite wordlength FIR digital filters is described. Examples of two optimal low-pass FIR finite wordlength filters are given and the results are compared with the results obtained by rounding the infinite wordlength coefficients. An analysis of the approach based on the results of more than 50 design cases is presented and the problem of optimal wordlength choice is discussed.

Abstract: An efficient two-stage algorithm is presented for designing finite-impulse response (FIR) filters that employ sums of signed-powers-of-two (SPT) coefficients. In the first stage, a prototype filter is designed using a fast time-domain approximation. This is followed, in the second stage, where the design problem is formulated as a dynamic-programming-like recursive optimization problem, by a trellis search that optimizes the filter's frequency response. The proposed search algorithm, which iteratively designs filters that employ an increasing number of SPT terms, provides a means to control the filter's implementation complexity. Design examples demonstrate that our algorithm is capable of producing filters having a better frequency response than existing methods while using fewer SPT terms. We also show that the proposed algorithm can be used to design special FIR filters such as matched transmit and receive filters employing sums of signed-powers-of-two coefficients. Also presented is a modified algorithm that further reduces the required number of adders in a filter by exploiting redundancies within the coefficients.

Abstract: The fast Fourier transform (FFT) algorithm has been used in a variety of applications in signal and image processing. In this article, a simple procedure for designing finite-extent impulse response (FIR) discrete-time filters using the FFT algorithm is described. The zero-phase (or linear phase) FIR filter design problem is formulated to alternately satisfy the frequency domain constraints on the magnitude response bounds and time domain constraints on the impulse response support. The design scheme is iterative in which each iteration requires two FFT computations. The resultant filter is an equiripple approximation to the desired frequency response. The main advantage of the FFT-based design method is its implementational simplicity and versatility. Furthermore, the way the algorithm works is intuitive and any additional constraint can be incorporated in the iterations, as long as the convexity property of the overall operations is preserved. In one-dimensional cases, the most widely used equiripple FIR filter design algorithm is the Parks-McClellan algorithm (1972). This algorithm is based on linear programming, and it is computationally efficient. However, it cannot be generalized to higher dimensions. Extension of our design method to higher dimensions is straightforward. In this case two multidimensional FFT computations are needed in each iteration.