Signal processing with orthonormalized exponentials

Signal processing with sinusuidal waveforms as basis functions has dominated the electrical engineering discipline. Yet, a large class of signals arising from natural processes may be more efficiently represented by exponentials with complex or purely real exponents, rather than by exponentials with purely imaginary exponents which is the case in the Fourier representation. This paper presents a method for orthonormalizing a set of expontials and a survey of signal processing with orthonormalized exponential functions. It is tutorial in nature. A method for finding an optimal set of exponentials for efficient representation of an ensemble of signals is also given.