Author_Institution :
Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA
Abstract :
Major continuous-time, discrete-time, and discrete Fourier-related transforms as well as Fourier-related series are discussed both with real and complex kernels. The complex Fourier transforms, Fourier series, cosine, sine, Hartley, Mellin, Laplace transforms, and z-transforms are covered on a comparative basis. Generalizations of the Fourier transform kernel lead to a number of novel transforms, in particular, special discrete cosine, discrete sine, and real discrete Fourier transforms, which have already found use in a number of applications. The fast algorithms for the real discrete Fourier transform provide a unified approach for the optimal fast computation of all discrete Fourier-related transforms. The short-time Fourier-related transforms are discussed for applications involving nonstationary signals. The one-dimensional transforms discussed are also extended to the two-dimensional transforms
Keywords :
Fourier transforms; Laplace transforms; Z transforms; data compression; discrete cosine transforms; fast Fourier transforms; signal processing; Fourier series; Fourier-related transforms; Hartley transforms; Laplace transforms; Mellin transforms; complex Fourier transforms; complex kernels; cosine transforms; discrete sine transforms; image processing; nonstationary signals; one-dimensional transforms; optimal fast computation; real discrete Fourier transforms; signal compression; sine transforms; special discrete cosine transforms; two-dimensional transforms; z-transforms; Discrete Fourier transforms; Discrete transforms; Fast Fourier transforms; Fourier series; Fourier transforms; Image coding; Image processing; Kernel; Partial differential equations; Signal processing;
