The discrete prolate spheroidal filter as a digital signal processing tool

Abstract

The d i s c r e t e prolate spheriodal (DPS) f i l t e r i s one of the class of nonrecursive f i n i t e impulse response (FIR) f i l t e r s . The DPS f i l t e r , f i r s t introduced by TUFTS and FRANCIS (19701, i s superior t o other f i l t e r s i n t h i s c l a s s i n that i t has maximum energy concentration i n the frequency passband and minimum ringing i n the t i m e domain. DPS f i l t e r properties, provide information required t o construct the f i l t e r , and compare the properties of t h i s f i l t e r with those of the more commonly used f i l t e r s of the same class. W e note that use of the DPS f i l t e r allows f o r p a r t i c u l a r l y useful statements of data time/frequency resolution "cell" values and t h a t overall it forms an especially useful t o o l for d i g i t a l signal processing.

Continuous quasiperiodic thermospheric waves over Arecibo

“…That is, they have a steadily decreasing response as the frequency is increased. Thus there is not a sharp distinction between passbands and stopbands, simply a smooth roll‐off as shown in Figure 3 of Mathews et al [1985]. Therefore DPS filters cannot reject and accept the desired frequency ranges as readily as filters based on a more ideal frequency response such as those based on Hamming windows.…”

Linear prediction for bandpass signals based on nonuniform past samples

“…The extended sampling theorem [8], p.281, gives the form of signal x(t) as (2) with constant k := 2T B/π and with the usual definition of sinc(t) as sin(πt)/(πt). The Nyquist criterion for the bandpass signal is less restrictive in the size of the sampling interval T. Sampling for bandpass signals allows for larger T than a criterion that ignored the particular nature of the spectrum of the signal and based the sampling on criterion for band-limited signals.…”

“…This was described for the DPSS in [2]. Just as for the standard DPSS vectors, the complete set of unit norm eigenvectors of matrix A 2 , see (12), for parameter τ are related to the corresponding set of vectors for parameter…”

“…The DPSS, [2], satisfy a three-term recurrence relation that is derived based on the construction of a tridiagonal matrix that commutes with the sinc matrix S, described above. There is a tridiagonal matrix [9] which shares the eigenvectors for a given sinc matrix, and is appropriate for very accurate calculation of the prediction coefficients for the bandlimited case [3].…”

A new 2D quadrature polar separable filter and its applicable to texture analysis

“…We shall say that a function f(t) is timelimited if (9) The other important conclusion of the uncertainty principle in signal analysis is that a function f(t) cannot be simultaneously bandlimited and timelimitedjl41, An important question is what bandlimited signal contains maximum energy when it is cut-off in the time domain? In other words, what signal has the shortest time duration for a given energe loss.…”