One of the limitations of the discrete Fourier transform (DFT), as used for frequency representation of discrete-time signals and frequency analysis of systems characterized by linear constant-coefficients difference equations, is that it provides spectral information at equally spaced points on the unit circle in the z-plane.
This work focuses on a generalization of DFT called the nonuniform discrete Fourier transform (NDFT), defined as samples of the z-transform of a finite-length sequence evaluated at arbitrarily chosen points on the z-plane.
In the first two chapters, the authors review the definition and main properties of the DFT, present some existing methods for the computation of samples of the z-transform at selected points in the z-plane, develop the basic concepts of the NDFT, and describe several techniques for computing the direct, inverse, and two-dimensional NDFT.
The following four chapters deal with NDFT applications, including the design of one- and two-dimensional finite-impulse response filters, the synthesis of antenna patterns with specified null radiation directions and dual-tone multifrequency signal decoding. All of these chapters report recent research and contain existing methods, proposed processing techniques, experimental results, and comparisons between the performances of DFT- and NDFT-based algorithms.
The conclusions presented in the last chapter underline the great potential of the NDFT in signal processing when a good choice of sample locations is achieved.
The authors present both the fundamentals of the nonuniform discrete Fourier transform and some of its present signal processing applications in an accessible manner. This makes the book a useful reference for researchers in the field.