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The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing

The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing

Hardcover

Series: The Springer International Engineering and Computer Science, Book 463

Technology & EngineeringGeneral Mathematics

ISBN10: 0792382811
ISBN13: 9780792382812
Publisher: Springer Nature
Published: Nov 30 1998
Pages: 208
Weight: 1.10
Height: 0.56 Width: 6.14 Depth: 9.21
Language: English
The growth in the field of digital signal processing began with the simulation of continuous-time systems in the 1950s, even though the origin of the field can be traced back to 400 years when methods were developed to solve numerically problems such as interpolation and integration. During the last 40 years, there have been phenomenal advances in the theory and application of digital signal processing. In many applications, the representation of a discrete-time signal or a sys- tem in the frequency domain is of interest. To this end, the discrete-time Fourier transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the discrete Fourier transform (DFT) which results in a finite- length sequence in the frequency domain. The DFT is simply composed of the samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, the samples of its z-transform at equally spaced points on the unit circle. The DFT provides information about the spectral contents of the signal at equally spaced discrete frequency points, and thus, can be used for spectral analysis of signals. Various techniques, commonly known as the fast Fourier transform (FFT) algorithms, have been advanced for the efficient com- putation of the DFT. An important tool in digital signal processing is the linear convolution of two finite-length signals, which often can be implemented very efficiently using the DFT.

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