Non-uniform discrete Fourier transform

About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.

Reduction of peak to average power ratio in multicarrier systems

Abstract: We describe an improved method for decreasing the probability of an unacceptably high peak-to-average power ratio in a signal to be transmitted by a Frequency Division Multiplexing (FDM) system, such as a discrete multitone (DMT) system. The method involves generating at least two alternative signal sequences, computing Fourier transforms of the respective alternative signal sequences, and selecting for transmission one of these sequences, based on the Fourier transform computations. More specifically, the selection of one sequence may be based, e.g., on the determination that the Fourier transform of that sequence has an acceptable peak power. Alternatively, a comparison may be made among the Fourier transforms of the respective signal sequences, and selection made of that sequence whose Fourier transform exhibits the lowest peak power.

The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus

Abstract: We introduce a fast Fourier transform on regular d-dimensional lattices. We investigate properties of congruence class representants, i.e. their ordering, to classify directions and derive a Cooley-Tukey-Algorithm. Despite the fast Fourier techniques itself, there is also the advantage of this transform to be parallelized efficiently, yielding faster versions than the one-dimensional Fourier transform. These properties of the lattice can further be used to perform a fast multivariate wavelet decomposition, where the wavelets are given as trigonometric polynomials. Furthermore the preferred directions of the decomposition itself can be characterised.

Mixed domain filtering of multidimensional signals

Abstract: The concept of multidimensional mixed domain transform/spatiotemporal (MixeD) filtering is extended beyond the discrete Fourier transform (DFT) to include other types of discrete sinusoidal transforms, including the discrete Hartley transform (DHT) and the discrete cosine transform (DCT). Two MixeD filter examples are given, one using the two-dimensional (2-D) DHT and the other using the 2-D DCT, to selectively enhance a 3-D spatially planar (SP) pulse signal. The authors define the notation and provide a review of the MixeD filter method. MD and partial P-dimensional discrete transform operators are defined, and the design of MixeD filters is discussed. MixeD filters based on the 2-D DHT and the 2-D DCT are designed to selectively enhance a 3-D SP pulse. Experimental verification of these 3-D SP MixeD filters is described. >

'Instant' Fourier transform

Abstract: The fast Fourier transform andd the fast Walsh transform are too slow for some real-time applications. For binary data, an 'instant' Fourier transform is based on harmonic analysis in a space of 2 n -tuples of 0s and 1s. Simple, modular logic finishes transforming 2n real-time serial binary data one clock pulse after the last datum arrives.

Discrete Fourier Transform and Signal Spectrum

Abstract: This chapter investigates discrete Fourier transform (DFT) and fast Fourier transform (FFT) and their properties; introduces the DFT/FFT algorithms to compute signal amplitude spectrum and power spectrum; and uses the window function to reduce spectral leakage. Finally, the chapter describes the FFT algorithm and shows how to apply FFT it to estimate a speech spectrum.