Prolate spheroidal digital filtering

Neelakantan, V. (1986) Prolate spheroidal digital filtering. Masters thesis, Memorial University of Newfoundland.

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Abstract

The use of Digital Prolate Spheroidal Wave Functions (DPSWF) in the field of digital filtering has increased steadily during the past decade. The unique property: that DPSWF provide maximum concentration of signal energy in the passband of a low-pass filter has been the basis of most of the work done in the area of digital filter design involving the prolate functions. The maximization of energy corresponds to the largest eigenvalue, which belongs to the lowest order DPSWF, and the energy concentration decreases as the order increases. -- It is, however, desirable to investigate the effect of higher order eigenfunctions in addition to the lowest order one on the filter characteristics and performance. This thesis is the outcome of such investigations. A suitably weighted linear combination of those DPSWF which are even functions of frequency is made to approximate an ideal low-pass characteristic in the minimum mean squared error (MMSE) sense. -- Results employing various numbers of even prolate functions are obtained and compared with each other and with the maximum energy concentration case. It is shown that the flatness of the passband of a low-pass filter is greatly improved with the number of even prolate functions while maintaining a tolerable loss of energy in the passband. -- One of the key features of the lowest order DPSWF, is that its side lobes are very low. This is a direct result of maximizing the concentration of energy within a certain interval. This feature is very useful for harmonic analysis problems. This is demonstrated by applying the prolate function as a window in harmonic analysis using discrete Fourier transform. The performance of the prolate function is compared to that of many other popular window functions, in the present work.

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