Signal Processing via Fourier-Bessel Series Expansion

摘要

In many cases it may not be desirable or even practical to represent a signal byits sample values directly or by an analytical function if a suitable function is available. For example, a signal may be determined by time domain sample values when the parameters of interest are more compact within the frequency domain. Many practical signals are highly redundant, both image and speech signals fall into this category, and it may be desirable and possibly necessary to represent the signal with a fewer number of samples for economy of storage and/or transmission bandwidth limitations. Whatever the desired goal the processing of signals can often be carried out more efficiently in another domain than that of the original signal. An obvious example here with the advent of hardware Fast Fourier Transform (FFT) devices is the widespread frequency domain processing of naturally occurring time domain signals. Pattern recognition techniques rely on the ability to generate a set of coefficients from the raw data (time domain samples) that are more compact (i.e. fewer samples) and we hope, are more closely related to the signal characteristics of interest. Clearly, if one is interested in frequency content, a Fourier series representation packs the frequency information in to fewer samples (Fourier series coefficients) than a time domain representation.