Title: On the interpolation function for classes of sampling theorems with non‐uniform sampling points
Abstract: Abstract A time waveform which is absolutely square integrable and whose Fourier spectrum is identically zero above a certain finite frequency is called a band‐limited waveform. This paper discusses a sampling theorem for a band‐limited waveform based on a set of sampling points. The waveform structure is such that a finite number of sampling points are periodically repeated. The following results are obtained. An interpolation formula which is sufficiently general is established for the sampling theorem of the discussed type. The necessary and sufficient condition is derived for the interpolation function in order that the interpolation formula apply to any band‐limited waveform. By this theorem, required interpolation functions can systematically be determined by the Fourier expansion coefficient, with respect to the angular frequency, of a finite number of two‐variable functions of time and angular frequency, called the generating variable. Then a special case of sampling theorem is considered, where the interpolation filter determined in correspondence to the interpolation function is time‐invariant, deriving the necessary and sufficient condition for the Fourier spectrum of the interpolation function (i.e., the frequency characteristics of the interpolation filter). Some detailed expressions are discussed for the interpolation function, which can easily make the Fourier spectrum continuous or smooth.
Publication Year: 1982
Publication Date: 1982-01-01
Language: en
Type: article
Indexed In: ['crossref']
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