Topic
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.
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TL;DR: In this article, the Fourier transform was used to analyze the self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent using the frequency domain using Fourier Transform.
Abstract: The self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent has been analysed in the frequency domain using the Fourier transform. Expression for the Fourier amplitude and phase spectra are derived. The Fourier amplitude and phase spectra are analysed so as to evaluate the parameters of the sheet. Application of this method on two anomalies (synthetic and field data) has given good results.
46 citations
TL;DR: This work presents the first all-optical nonlinear joint transform correlator based on a square-law receiver in the Fourier plane, which is the first time to the authors' knowledge that photorefractives or real-time holography has been used in the correlation of the phase-only information.
Abstract: A fully parallel, self-aligning, nonlinear and all optical joint transform correlator utilizes a photorefractive four wave mixer positioned to record the joint transform spectrum interfering with a reference beam together with a phase conjugator which directs a readout beam at the four wave mixer. The signal readout of the mixer is Fourier transformed and can be recorded upon an image sensor to detect the correlation spots indicating the degree of similarity of the two input images.
46 citations
TL;DR: The discrete Gabor (1946) transform algorithm is introduced that provides an efficient method of calculating the complete set of discreteGabor coefficients of a finite-duration discrete signal from finite summations and to reconstruct the original signal exactly from the computed expansion coefficients.
Abstract: The discrete Gabor (1946) transform algorithm is introduced that provides an efficient method of calculating the complete set of discrete Gabor coefficients of a finite-duration discrete signal from finite summations and to reconstruct the original signal exactly from the computed expansion coefficients. The similarity of the formulas between the discrete Gabor transform and the discrete Fourier transform enables one to employ the FFT algorithms in the computation. The discrete 1-D Gabor transform algorithm can be extended to 2-D as well. >
46 citations
Patent•
02 Oct 1997TL;DR: In this paper, a system and method for demodulation of an RF signal on a transmission channel is provided, where the RF signal is demodulated to baseband as an in-phase (I) data signal and a quadrature (Q) signal, and a time domain guard interval is provided in the captured first blocks of I and Q data.
Abstract: A system and method for demodulation of an RF signal on a transmission channel is provided. The RF signal is demodulated to baseband as an in-phase (I) data signal and a quadrature (Q) data signal. A first block of I data is captured and a first block of Q data is captured. A time domain guard interval is provided in the captured first blocks of I and Q data. A complex discrete Fourier transform is performed on the captured first I and Q data blocks. An inverse frequency response for the transmission channel is determined. The inverse frequency response is multiplied by the complex discrete Fourier transform of the guard-interval protected first I and Q data blocks to generate a frequency domain product signal. An inverse Fourier transform on the product of the multiplying step is performed to generate a first equalized time domain signal. In a preferred embodiment, the method also includes using an overlapped Fourier transform and discarding a first portion of each equalized time domain signal.
46 citations
TL;DR: A special class of even-symmetric periodic signals is introduced that their real-valued Fourier coefficients can be calculated by forming a weighted average of the signal values using integer-valued coefficients.
Abstract: A special class of even-symmetric periodic signals is introduced. The most distinctive feature of these signals is that their real-valued Fourier coefficients can be calculated by forming a weighted average of the signal values using integer-valued coefficients. The signals arise from number-theoretic concepts concerning a class of functions called even arithmetical functions. The integer-valued weighting coefficients, being sums of complex roots of unity, are the Ramanujan sums and may be computed recursively or through closed-form arithmetical relations. The recursive method of computation is based on the cyclotomic polynomials and is described in detail. If the signal values are integers, the computation of the discrete Fourier transform (DFT) coefficients of this class of signals can be performed in an exact quantization-error-free manner by performing arithmetical operations on integers. The theoretical development is supplemented by concrete examples.
46 citations