A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time- and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made equiripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design examples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach.

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Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

This paper introduces a new class of linear-phase FIR Nyquist ( N th-band) filters composed of cascaded FIR subfilters with different periodicities in the frequency domain. Each one of the subfilters is itself a Nyquist filter or an N th-band filter. - The composite filters have zero intersymbol interference and they provide a Chebyshev stopband behavior, thereby band-limiting the pulses optimally. A computationally efficient Remez-type procedure is presented for simultaneously optimizing the subfilters. This algorithm is equally applicable to the design of conventional single-stage FIR Nyquist ( N th-band) filters. Examples demonstrate that the proposed multistage filters provide significant advantages over equivalent IIR filters and single-stage FIR filters in terms of reduced multiplication rate and reduced number of multipliers. In addition, it is shown that, in the case of single-stage implementations, the proposed algorithm gives FIR Nyquist filters having higher selectivities than those which have been designed using other methods.

A class of FIR Nyquist (Nth-band) filters with zero intersymbol interference

The design of a (FIR) finite-impulse-response digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the Steiglitz's program [1] is modified and then used to design a class of constrained FIR digital filters. This class includes pulse shaping filters, N th band filters and nonuniform tap spacing filters, where some of the filter coefficients are constrained to zero. The advantage of the present approach, as compared to other methods, with regard to design speed and filter optimality and performance, are described, and illustrated by means of examples.

https://ieeexplore.ieee.org/iel5/31/23567/01085702.pdf

Design of optimal Nyquist, partial response, Nth band, and nonuniform tap spacing FIR digital filters using linear programming techniques

A new infinite impulse response (IIR) Nyquist filter with zero intersymbol interference is proposed. The necessary and sufficient conditions for the transfer function are obtained. The proposed IIR Nyquist filter requires only frequency-domain optimization. Multistep optimization, using the iterative Chebyshev approximation, is proposed. This method is able to design a new kind of IIR Nyquist filter with the minimum order. Numerical examples for 30- and 15-percent rolloff rates are illustrated. From these examples, it is confirmed that the IIR approach can reduce the filter order and hardware size, compared with the conventional finite impulse response (FIR) Nyquist filters. Its efficiency becomes marked for high Q Nyquist filters.

A new IIR Nyquist filter with zero intersymbol interference and its frequency response approximation

A high efficiency special purpose linear programming algorithm for FIR filter design is introduced, This algorithm incorporates FFT and FIR zero-phase filters to assist in the computation. Compared to the general purpose linear programming, this special purpose linear programming produces large savings in the computing cost when used to design FIR filters. The savings increase with the length of the filter being designed.

Efficient special purpose linear programming for FIR filter design

The use of time-domain specifications is demonstrated for designing frequency-sampling digital filters that generate data pulses for transmission over an ideal band-limited channel. Desired characteristics of the transmitted pulse are used to formulate the set of constraint equations and objective function used in linear programming to obtain an optimum set of filter coefficients, i.e., frequency samples {| H(k) |} - The constraints are the amplitudes assigned to the set of regularily spaced samples taken from the pulse. The objective function is either to minimize the maximum absolute error between desired and generated pulse samples over the specified pulse duration or to provide zero crossings in the transmitted pulse with near-zero slope in order to protect against intersymbol interference (ISI) due to timing error (jitter).

R. Houts

Papers

Time-domain design of frequency-sampling digital filters for pulse shaping using linear programming techniques