Abstract :
The efficiency for signal representation of the angular prolate spheroidal wave function, particularly the two sets Sol(1, t) and Sol(8, t) is discussed Six signal waveforms are considered: rectangular, triangular, trapezoidal, exponential, Gaussian, and cosine-squared. For each, a representation is made in terms of the two sets above and also the Fourier cosine functions. As the number of terms of the representation increases, the approximation gets better. A measure of the ¿goodness¿ of the approximation is the percentage of the total signal energy represented by the finite expansion, over a fixed, finite time interval. The angular prolate spheroidal wave functions are a very efficient orthogonal set in this sense. Their principal advantage over Fourier cosine functions occurs for cases whereby only a very few terms of the expansion are to be used to approximate a signal shape.
