Book ChapterDOI
Transforms and Transform Properties
Douglas F. Elliott
- pp 1-53
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TLDR
In this article, the authors provide an overview of transforms and transform properties for the analysis of data sequences, and discuss the reason for the periodicity of the discrete-time spectrum and presents DTFT properties.Abstract:
Publisher Summary This chapter provides an overview of transforms and transform properties. It reviews the nature of the sampled data and transforms and transform properties for the analysis of data sequences. The integrals defining the series coefficients correspond to the inverse discrete-time Fourier (IDTFT) and considers one- and two-dimensional series. The aliasing phenomenon leads to a periodic spectrum for data sequences so that the spectrum has a Fourier representation in terms of the data. This representation can be found from the data by using the discrete-time Fourier transform (DTFT). The DTFT is generalized to the z-transform, which is a powerful tool for data sequence analysis. The chapter discusses the reason for the periodicity of the discrete-time spectrum and presents DTFT properties. It also reviews the discrete Fourier transform (DFT) and highlights the Laplace transform. The chapter reviews discrete-time random sequences and discusses correlation and covariance sequences and their power spectral densities.read more
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Proceedings ArticleDOI
Fast Spectral Formulations of Thin Plate Laser Heating with GPU Implementation
TL;DR: Two different schemes that translate the problem of laser beam heating of metal plates into equivalent FFT problems are presented, showing significant improvements in terms of executions times, being 100× faster than current state-of-the-art algorithms.
Book ChapterDOI
Exploratory Spectral Analysis of Time Series
TL;DR: Over 20 years have passed since the publication of a book by Box and Jenkins where the principles of time series analysis and modeling were formulated and has become the standard procedure for time series modeling and analysis.
References
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Journal ArticleDOI
The fast Fourier transform algorithm: Programming considerations in the calculation of sine, cosine and Laplace transforms☆
TL;DR: The problem of establishing the correspondence between the discrete transforms and the continuous functions with which one is usually dealing is described and formulas and empirical results displaying the effect of optimal parameters on computational efficiency and accuracy are given.
Journal ArticleDOI
On the use of symmetry in FFT computation
TL;DR: This paper shows how a similar approach can be used for sequences which are known to have only odd harmonics, and is shown to be essentially the dual of the known method for time symmetry.