Biomedical signal processing (in four parts). Part 2. The frequency transforms and their inter-relationships.

ABSTRACT

This is the second in a series of four tutorial papers on biomedical signal processing, and it concerns the relationships between commonly used frequency transforms. It begins with the Fourier series and Fourier transform for continuous time signals and extends these concepts for aperiodic discrete time data and then periodic discrete time data. The Laplace transform is discussed as an extension of the Fourier transform. The z-transform is introduced and the ideas behind the chirp-z transform are described. The equivalence between the time and frequency domains is described in terms of Parseval's theorem and the theory of convolution. The use of the FFT for fast convolution and fast correlation is described for both short recordings and long recordings that must be processed in sections.