Abstract
The Fourier representation of analog signals was discussed in the previous chapter. This representation is now extended to data sequences, and digital signals. To this end, the discrete Fourier transform (DFT) is defined and several of its properties are developed. Specifically, the convolution and correlation theorems are described and the spectral properties such as amplitude, phase, and power spectra are developed. By illustrating the 2-dimensional DFT, it is shown that the DFT can be extended to multiple dimensions. Finally, the concepts of time-varying Fourier power and phase spectra are introduced.
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Ahmed, N., Rao, K.R. (1975). Fourier Representation of Sequences. In: Orthogonal Transforms for Digital Signal Processing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45450-9_3
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DOI: https://doi.org/10.1007/978-3-642-45450-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45452-3
Online ISBN: 978-3-642-45450-9
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