Orthogonality of exponential transients

It is shown that simple orthogonal representations exist for signals which are of a decaying, rather than purely sinusoidal nature. This orthogonality is expressed in terms of a weighting function. It is shown that alternate, nonuniform sampling techniques for representation and processing of these signals are appropriate. Using this nonuniform sampling scheme, a simple discrete representation, very much like the discrete Fourier transform, can be derived. Hence, it is pointed out that traditional, frequency-spectrum-based techniques for signal analysis may be replaced by methods that are better suited for the specific decaying signal type.<>