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. 

Continuous-time Fourier analysis: 
Fourier series is an approximation process where any general (periodic or aperiodic) signal is expressed as sum of harmonically related sinusoids. It gives us a frequency domain (or spectral) representation. If the signal is periodic Fourier series represents the signal in the entire interval (-∞, ∞). i.e. Fourier series can be generalized for periodic signals only. 
 

Signal Sampling and Reconstruction:
The process of sampling is a bridge between continuous-time and discrete-time systems. Sampling is a process of converting a continuous-time signal to a discrete-time signal, and under certain conditions, the continuous-time signal can be completely recovered from its sampled sequence.