Discrete-Time Fourier Transform (DTFT):
In this chapter, we present the Fourier analysis in the context of discrete-time signals (sequences) and systems. The Fourier analysis plays the same fundamental role in discrete time as in continuous time. As we will see, there are many similarities between the techniques of discrete-time Fourier analysis and their continuous-time counterparts, but there are also some important differences.
Z-Transform:
The discrete-time counterpart of Laplace transform is z-transform. The frequency domain analysis of discrete-time system allows us to represent any arbitrary signal x[n] as a sum of exponentials of the form zn. There are two varieties of z-transform: bilateral and unilateral. The bilateral one, also known as two-sided z-transform, can handle all causal and non-causal signals. It provides insights about system's characteristics such as stability, causality and frequency response. The unilateral one, also known as one-sided z-transform, can handle only causal signals.
