Publisher Summary This chapter discusses Fourier analysis and associated transform methods for both discrete-time and continuous-time signals and system. Fourier methods are based on using real or complex sinusoids as basic functions, and they allow signals to be represented in terms of sums of sinusoidal components. In order for a digital computer to manipulate a signal, the signal must be sampled at a chosen sampling rate, 1/TS, giving rise to a set of numbers called a sequence. Special analysis and many other applications often require discrete Fourier transforms (DFTs) to be performed on data sequences in real time and on contiguous sets of input samples. The theory of discrete-time, linear, time invariant systems forms the basis for digital signal processing, and a discrete-time system performs an operation on the input signal according to defined criteria to produce a modified output signal. The z-transform of the sum of two sequences multiplied by arbitrary constants is the sum of the z-transforms of the individual sequences, where Z represents the z transform operator. Data windows are introduced to smooth out the ripples introduced by the rectangular window.