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.

Signals, systems, and transforms

Abstract: (NOTE: Each chapter begins with an Introduction and ends with a Summary and Problems). 1. Overview of Signals and Systems. Signals. Systems. 2. Continuous-Time and Discrete-Time Signals. PART A Continuous-Time Signals. Basic Continuous -Time Signals. Modification of the Variable t. Continuous-Time Convolution. PART B Discrete-Time Signals. Basic Discrete-Time Signals. Modification of the Variable n. Discrete-Time Convolution. 3. Linear Time-Invariant Systems. PART A Continuous-Time Systems. System Attributes. Continuous-Time LTI Systems. Properties of LTI Systems. Differential Equations and Their Implementation. PART B Discrete-Time Systems. System Attributes. Discrete-Time LTI Systems. Properties of LTI Systems. Difference Equations and the Their Implementation. 4. Fourier Analysis for Continuous-Time Signals. The Eigenfunctions of Continuous-Time LTI Systems. Periodic Signals and the Fourier Series. The Continuous-Time Fourier Transform. Properties and Applications of the Fourier Transform. APPLICATION 4.1 Amplitude Modulation. APPLICATION 4.2 Sampling. 5.Frequency Response of LTI Systems. APPLICATION 4.3 Filtering. 5. The Laplace Transform. The Region of Convergence. The Inverse Laplace Transform. Properties of the Laplace Transform. The System Function for LTI Systems. Differential Equations. APPLICATION 5.1 Butterworth Filters. Structures for Continuous-Time Filters. Appendix 5A The Unilateral Laplace Transform. Appendix 5B Partial-Fraction Expansion for Multiple Poles. 6. The z Transform. The Eigenfunctions of Discrete-Time LTI Systems. The Region of Convergence. The Inverse z Transform. Properties of the z Transform. The System Function to LTI Systems. Difference Equations. APPLICATION 6.1 Second-Order IIR Filters. APPLICATION 6.2 Linear-Phase FIR Filters. Structures for Discrete-Time Filters. APPENDIX 6A The Unilateral z Transform. APPENDIX 6B Partial-Fraction Expansion for Multiple Poles. 7. Fourier Analysis for Discrete-Time Signals. The Discrete-Time Fourier Transform. 2.Properties of the DTFT. APPLICATION 7.1 Windowing. 3.Sampling. 4.Filter Design by Transformation. 5.The Discrete Fourier Transform/Series. APPLICATION 7.2 FFT Algorithm. 8. State Variables. Discrete-Time Systems. Continuous-Time Systems. Operational-Amplifier Networks. Bibliography. Index.

On the divergence of Fourier series

Abstract: 1. By a well known theorem of Kolmogoroff there is a function whose Fourier series diverges almost everywhere. Actually, Kolmogoroff's proof was later generalized so that the Fourier series diverged everywhere [2, p. 175]; but we shall be concerned only with the almost everywhere theorem here. The proof involves rather severe restrictions on the orders of the partial sums which are shown to diverge. The following problem connected with this theorem was suggested to the author by Professor A. Zygmund. Given a sequence I p, } of positive integers increasing to oo, can an integrable function f on (0, 2r) be constructed so that the partial sums of its Fourier series of order p, diverge almost everywhere ? The object of our paper is to give an affirmative answer to this question. Let sp(x; f) denote the pth partial sum of the Fourier series of the function f at the point x.

Weighting effect on the discrete time Fourier transform of noisy signals

Abstract: The effect of weighting on the uncertainty of the discrete time Fourier transform (DTFT) samples of a signal corrupted by additive noise is investigated. Making very weak assumptions, it is shown how the adopted window sequence and the autocovariance function of the noise affect the second-order stochastic moments of the frequency-domain data. The relationship obtained extends the results reported in the literature and is useful in many frequency-domain estimation problems. It is shown how the knowledge of the second-order moments of the transform has allowed the application of the least squares technique for the estimation of the parameters of a multifrequency signal in the frequency-domain. The estimator obtained is very useful when high-accuracy results are required under real-time constraints. The procedure exhibits a better accuracy than similar frequency-domain methods proposed in the literature. >

Modified Fourier transform method for interferogram fringe pattern analysis.

Abstract: A modified Fourier transform method for interferogram fringe pattern analysis is proposed. While it retains most of the advantages of the Fourier transform method, the new method overcomes some drawbacks of the previous method. It eliminates the assumptions of slowly varying phase variation in the test section and the constant spatial carrier frequency. It also extends the frequency bandwidth and avoids phase distortion caused by discreteness of the sampling frequency. Both numerical simulation and experimental examination are performed to evaluate the performance of the method.