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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