Topic
Discrete-time Fourier transform
About: Discrete-time Fourier transform is a research topic. Over the lifetime, 5072 publications have been published within this topic receiving 144643 citations. The topic is also known as: DTFT.
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TL;DR: In this article, it was shown that a one-dimensional or multidimensional sequence is uniquely specified under mild restrictions by its signed Fourier transform magnitude (magnitude and 1 bit of phase information).
Abstract: In this paper, we show that a one-dimensional or multidimensional sequence is uniquely specified under mild restrictions by its signed Fourier transform magnitude (magnitude and 1 bit of phase information). In addition, we develop a numerical algorithm to reconstruct a one-dimensional or multidimensional sequence from its Fourier transform magnitude. Reconstruction examples obtained using this algorithm are also provided.
88 citations
TL;DR: The 3D discrete definition of the Radon transform is shown to be geometrically faithful as the planes used for summation exhibit no wraparound effects and there exists a special set of planes in the 3D case for which the transform is rapidly computable and invertible.
88 citations
TL;DR: The base 8 algorithms described in this paper allow one to perform as many base 8 iterations as possible and then finish the computation by performing a base 4 or a base 2 iteration if one is required, which preserves the versatility of the base 2 algorithm while attaining the computational advantage of thebase 8 algorithm.
Abstract: 1. Introduction. Cooley and Tukey stated in their original paper [1] that the Fast Fourier Transform algorithm is formally most efficient when the number of samples in a record can be expressed as a power of 3 (i.e., N = 3m), and further that there is little efficiency lost by using N = 2m or N = 4™. Later, however, it was recognized that the symmetries of the sine and cosine weighting functions made the base 4 algorithms more efficient than either the base 2 or the base 3 algorithms [2], [3]. Making use of this observation, Gentleman and Sande have constructed an algorithm which performs as many iterations of the transform as possible in a base 4 mode, and then, if required, performs the last iteration in a base 2 mode. Although this "4 + 2" algorithm is more efficient than base 2 algorithms, it is now apparent that the techniques used by Gentleman and Sande can be profitably carried one step further to an even more efficient, base 8 algorithm. The base 8 algorithms described in this paper allow one to perform as many base 8 iterations as possible and then finish the computation by performing a base 4 or a base 2 iteration if one is required. This combination preserves the versatility of the base 2 algorithm while attaining the computational advantage of the base 8 algorithm.
88 citations
01 Dec 1974
TL;DR: In this article, the Fourier analysis of real-valued stationary discrete time series is studied and the power spectrum, the fitting of finite parameter models, and the identification of linear time invariant systems are discussed.
Abstract: This paper begins with a description of some of the important procedures of the Fourier analysis of real-valued stationary discrete time series. These procedures include the estimation of the power spectrum, the fitting of finite parameter models, and the identification of linear time invariant systems. Among the results emphasized is the one that the large sample statistical properties of the Fourier transform are simpler than those of the series itself. The procedures are next generalized to apply to the cases of vector-valued series, multidimensional time series or spatial series, point processes, random measures, and finally to stationary random Schwartz distributions. It is seen that the relevant Fourier transforms are evaluated by different formulas in these further cases, but that the same constructions are carried out after their evaluation and the same statistical results hold. Such generalizations are of interest because of current work in the fields of picture processing and pulse-code modulation.
87 citations
Book•
01 Jan 2003
TL;DR: In this paper, the authors present an analysis of the Fourier analysis of Discrete Time Signals (DTFT) and demonstrate that the DTFT can be used to estimate the spectral properties of continuous time signals.
Abstract: 1. FUNDAMENTALS OF SIGNALS AND SYSTEMS. Signals. Systems. Fourier Analysis of Discrete Time Signals. Fourier Analysis of Continuous Time Signals. 2. DISCRETE TIME PROCESSING OF CONTINUOUS TIME SIGNALS. Introduction. Structure of a Digital Filter. Frequency Domain Analysis of a Digital Filter. Quantization Errors. Prediction-Based Sampling Methods: Sigma and Sigma-Delta Modulation. 3. FOURIER ANALYSIS OF DISCRETE TIME SIGNALS. Introduction. Discrete Time Fourier Transform (DTFT). Discrete Fourier Transform (DFT). The DFT as an Estimate of the DTFT. DFT for Spectral Estimation. DFT for Convolution. DFT/DCT for Compression. The Fast Fourier Transform (FFT). 4. DIGITAL FILTERS. Introduction. Ideal Versus Nonideal Filters. Finite Impulse Response (FIR) Filters. Infinite Impulse Response (IIR) Filters. 5. DIGITAL FILTERS IMPLEMENTATION. Introduction. Elementary Operations. State Space Realization of Digital Filters. Robust Implementation of Digital Filters. Robust Implementation of Equiripple FIR Filters. 6. MULTIRATE DIGITAL SIGNAL PROCESSING: FUNDAMENTALS. Introduction. Statement of the Problem and Definitions. Analysis of Downsampling and Upsampling. Sampling Rate Conversion by a Rational Factor. Multistage Implementation of Digital Filters. Efficient Implementation of Multirate Systems. Application of Multirate DSP: Digital-to-Analog Conversion. Sampling Frequency and Quantization Error. 7. DFT FILTER BANKS AND TRANSMULTIPLEXERS. Introduction. DFT Filter Banks. Maximally Decimated DFT Filter Banks and Transmultiplexers. Transmultiplexers. Application of Transmultiplexers to Digital Communication Modulation. 8. MAXIMALLY DECIMATED FILTER BANKS. Introduction. Vector Spaces. Two-Channel Perfect Reconstruction Conditions. Design of Perfect Reconstruction Filter Banks with Real Coefficients. Lattice Implementation of Orthonormal Filter Banks. Application to an Audio Signal. 9. TIME FREQUENCY EXPANSION: AN INTRODUCTION. Introduction. The Short Time Fourier Transform (STFT). The Gabor Transform (GT). The Wavelet Transform. Recursive Multiresolution Decomposition. APPENDIXES. INDEX.
87 citations