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Signals on ℤ(T)/ℤ(Tp)

  • Gianfranco Cariolaro

Abstract

Discrete-time periodic signals, i.e., signals defined on ℤ(T)/ℤ(T p ), have become important because they are the only class of one-dimensional signals that can be processed directly by a computer, for the reason that they are fully specified by a finite number of values N=T p /T. This assertion holds also in the frequency domain, where the dual group is
$$\mathbb{Z}(F)/\mathbb{Z}(F_p),$$
and the Fourier transform is a discrete-frequency periodic function that is specified by the same number of values N=F p /F. It is worth insisting on the fact that all other 1D signals (continuous- time, discrete-time) when simulated on a digital computer must be related to and approximated by signals on ℤ(T)/ℤ(T p ).

In this chapter signals on ℤ(T)/ℤ(T p ) are developed with the purpose of formulating the background for a study of the signals with a digital computer. Implementation techniques will be seen in the next chapter. In particular, the discrete Fourier transform (DFT) and the discrete cosine transform (DCT) will be studied in great detail.

Keywords

Frequency Domain Discrete Cosine Transform Discrete Fourier Transform Periodic Signal Real Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag London Limited 2011

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