ABSTRACT
The representation of periodic signals becomes the discrete-time Fourier series (DTFS), and for aperiodic signals, it becomes the discrete-time Fourier transform(DTFT). The motivation for representing discrete-time signals as a linear combination of complex exponentials is identical in both continuous-time and discrete-time. The complex exponentials are eigenfunctions of linear, time-invariant systems, and consequently, the effect of an LTI system on each of these basic signals is simply the amplitude change. An LTI system is completely considered by a spectrum applies at each frequency. In representing discrete-time periodic signals through the Fourier series, use harmonically related complex exponentials with fundamental frequencies. In this chapter will discuss the discrete-time Fourier transform and its application in digital signal processing.
