Discrete sine transform

About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.

Discrete cosine transforms on quantum computers

Abstract: A classical computer does not allow the calculation of a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size N/spl times/N and types I, II, III and IV with as little as O(log/sup 2/N) operations on a quantum computer; whereas the known fast algorithms on a classical computer need O(N logN) operations.

Computing the Hilbert transform on the real line

Abstract: We introduce a new method for computing the Hilbert transform on the real line. It is a collocation method, based on an expansion in rational eigenfunctions of the Hilbert transform operator, and implemented through the Fast Fourier Transform. An error analysis is given, and convergence rates for some simple classes of functions are established. Numerical tests indicate that the method compares favorably with existing methods

On coding and filtering stationary signals by discrete Fourier transforms (Corresp.)

Abstract: This correspondence concerns real-time Fourier processing of stationary data and examines the widespread belief that coefficients of the discrete Fourier transform (DFT) are "almost" uncorrelated. We first show that any uniformly bounded N \times N Toeplitz covariance matrix T_N is asymptotically equivalent to a nonstandard circulant matrix C_N derived from the DFT of T_N . We then derive bounds on a normed distance between T_N and C_N for finite N , and show that \mid T_N - C_N \mid ^ 2 = O(1/N) for finite-order Markov processes. Finally we demonstrate that the performance degradation resulting from the use of DFT (as opposed to Karhunen-Loeve expansion) in coding and filtering is proportional to \mid T_N - C_N \mid and therefore vanishes as the inverse square root of the block size N when N \rightarrow \infty .

A generalized concept of frequency and some applications

Abstract: The system of sine and cosine functions has been distinguished historically in communications. Whenever the term frequency is used, reference is made implicitly to these functions; hence the generally used theory of communication is based on the system of sine and cosine functions. In recent years other complete systems of orthogonal functions have been used for theoretical investigations as well as for equipment design. Analogs to Fourier series, Fourier transform, frequency, power spectra, and amplitude, phase, and frequency modulation exist for many systems of orthogonal functions. This implies that theories of communication can be worked out on the basis of these systems. Most of these theories are of academic interest only. However, for the complete system of the orthogonal Walsh functions, the implementation of circuits by modem semiconductor techniques appears to be competitive in a number of applications with the implementation of circuits for the system of sine and cosine functions.