The discrete prolate spheroidal filter as a digital signal processing tool

The discrete prolate spheroidal (DPS) filter is one of the class of nonrecursive finite impulse response (FIR) filters. The DPS filter, first introduced by Tufts and Francis [1], is superior to other filters in this class in that it has maximum energy concentration in the frequency passband and minimum ringing in the time domain. Slepian [2] gives a complete discussion of DPS function properties. We give a mathematical development of the DPS filter properties, provide information required to easily and accurately construct even many coefficient filters, and compare the properties of this filter with those of the more commonly used filters of the same class. We note that use of the DPS filter allows for particularly useful statements of data time/frequency resolution "cell" values and that overall it forms an especially useful, though little known tool for digital signal processing.