Approximate Representation of Bandlimited Signals by Elementary Functions

摘要

An approximate representation of bandlimited signals is constructed which resembles the spherical Bessel function representation. Here, however, the coefficients of the expansion are derived from those of the prolate function expansion and thus require knowledge of the signal over only a finite time interval. An analytic approximation to the Fourier transform of the signal is presented, and the Taylor series expansion of the transform in truncated. The error of the representation is bound both from above and below, and the procedure is structured so that, aside from known constant values that must be computed just once for the given class of signals, the only computation required is that of the coefficients in the prolate function expansion of the signal.