The Fourier transform in biomedical engineering. Dedicated to the memory of Richard H. T. Bates. With contributions from Jason H. T. Bates, G. Bruce Pike and Patrice Munger (Q1273593)

The authors state that they ``wanted to produce a book that would be comprehensible without extensive reliance on mathematics.'' Consequently many important mathematical results relevant to biomedical applications of the Fourier transform (FT) are presented but are supported only by verbal or pictorial arguments. This approach shows the reader the significance of the results but makes their practical use difficult, many examples of their practical application notwithstanding. Various aspects of the one-dimensional FT are reviewed including linearity, minimum sampling rates, digital filtering, convolution, power spectra, and system parameter identification. Two-dimensional FT's are examined with special emphasis on their application to tomography. A thorough discussion of the use of the FT in magnetic resonance imaging includes a review of the underlying physics. Wavelet analysis is introduced as an extension of Fourier analysis which allows for compact rather than extended basis functions. Much of this material has to do with multiresolution analysis, which facilitates studying a signal or function at different scales. Finally methods of computation of the discrete FT, the comb function, and the fast FT are treated.