Abstract
This chapter discusses the transform domain representation of discrete-time sequences by discrete-time Fourier series (DTFS) and discrete-time Fourier transform (DTFT) in which a discrete-time sequence is mapped into a continuous function of frequency. We first obtain the discrete-time Fourier series (DTFS) expansion of a periodic sequence. The periodic convolution and the properties of DTFS are discussed. The Fourier transform domain representation of discrete-time sequences are described along with the conditions for the existence of DTFT and its properties. Later, the frequency response of discrete-time systems, frequency domain representation of sampling process, and reconstruction of band-limited signals from its samples are discussed.
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Further Reading
Morrison, N.: Introduction to Fourier Analysis. Wiley, New York (1994)
Mitra, S.K.: Digital Signal Processing. McGraw-Hill, New York (2006)
Oppenheim, A.V., Schafer, W.: Discrete-Time Signal Processing, 2nd edn. Prentice-Hall, Upper Saddle River (1999)
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Rao, K.D. (2018). Frequency Domain Analysis of Discrete-Time Signals and Systems. In: Signals and Systems. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-68675-2_7
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DOI: https://doi.org/10.1007/978-3-319-68675-2_7
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-68674-5
Online ISBN: 978-3-319-68675-2
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