Showing papers by "Mohammed Abo-Zahhad published in 1996"

Arbitrary amplitude and linear phase approximations for non‐prototype ladder and lattice wave digital filters

Abstract: Two different approaches are introduced for the design of non-prototype ladder and lattice wave digital filters (WDFs) exhibiting arbitrary amplitude in the baseband (passband, transition band and stopband) and linear phase in the passband. The first approach is based on the phase correction of a minimum phase lattice (or ladder) WDF designed to satisfy the amplitude specifications in the three bands. In the second approach the amplitude and phase requirements are approximated simultaneously. It is devoted to the design of a lattice WDF that is constructed from the parallel arrangement of two allpass subfilters. The design procedure relies on preconstructing one of the subfilters to have exact linear phase at all frequencies and constructing the other to interpolate an arbitrary phase at a set of frequencies distributed all over the baseband. The hidden relationship between the amplitude and phase functions of the filter is utilized to approximate both of them. The approximation problem is solved by applying an interpolation technique combined with the Remez exchange algorithm. Prototype filters with amplitude specifications in the passband and stopband and phase specifications in the passband are also considered as special cases. Design examples are presented to show the efficiency of the two methods.

Filter designer: a complete design and synthesis program for lumped, wave-digital, FIR and IIR filters

Abstract: An interactive filter design program suitable for both experts and non-experts is described. It can be used for the design and synthesis of 64 filter families. These include: lumped, wave-digital (WD) FIR and IIR filters where each may be lowpass, highpass, band rejection, bandpass or phase corrector. Four amplitude approximation functions are available for all these cases; namely Butterworth, Chebyshev, inverse Chebyshev and elliptic approximation functions. Although it operates in both batch and interactive modes, this paper deals exclusively with the interactive mode which is somewhat more general and very easy to use. The filter designer offers superior accuracy and flexibility in manipulating filters with different specifications and network realizations. The synthesized networks are in the form of an LC ladder for lumped filters; lattice and bireciprocal for wave-digital filters: direct form for FIR filters as well as direct, cascade and parallel realizations for IIR filters. Utilities are given for the analysis of the amplitude, phase and group delay for all possible filter designs. In addition, pole-zero patterns and network realization are available in both numerical and graphical formats. Examples illustrating different design and synthesize capabilities are given.

On optimal filters with maximum number of constraints on amplitude and phase characteristics

Abstract: For optimal filters exhibiting specified amplitude and phase (or group delay) characteristics, it is required that all the free parameters of the transfer function be used for the approximation. To achieve this requirement, the number of constraints on the amplitude and phase characteristics is defined first on general interpolation bases. Constant or arbitrarily prescribed lowpass or bandpass group delay and amplitude characteristics are approximated in the maximally flat, ripple or mixed sense for lumped filters, whereas highpass and band rejection characteristics are also considered for distributed or sampled data filters. The relationship between the number of free parameters and the number of amplitude and phase constraints for a given degree is derived for non-reciprocal as well as for reciprocal lossy and reciprocal reactant cases. Conditions are derived for the distribution of the free parameters between the passband and stopband amplitude and phase characteristics for transfer functions with Hurwitzian denominator and also for monotonic amplitude characteristics in the transition band. Some published separate and simultaneous approximation methods are evaluated and compared on the above bases. It is pointed out that some of these methods do not satisfy the above requirements, although the optimal solution would exhibit higher performances.