Fractional Sampling using the Asynchronous Shah with application to LINEAR PHASE FIR FILTER DESIGN
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چکیده
We investigate the fundamental process of sampling using an impulse train, called the shah function [Bracewell], that is skewed in time by a constant offset relative to absolute time 0. We observe that when an originating analog signal is bandlimited, there is little difference between fractionally timeshifting the corresponding sequence, and synchronously sampling the time-shifted analog signal. We use these results to explain a curious parallel in the theoretical analysis of Types II and IV linear phase FIR (finite impulse response) filters that is manifest by an apparent 4π-periodicity in the "generalized" [O&S] linear amplitude and phase.
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