The Discrete Fourier Transform

As discussed in Section 1.1.2, the design of a DSP system basically involves two fundamental tasks, namely, the analysis of the input signal and the design of a processing system to give the desired output. There are several different mathematical tools for carrying out these two tasks. A time-domain approach was presented in Chapter 1, where a sampled input signal was represented by a weighted unit-impulse train and a DSP system was described by either a general difference equation or a unit-impulse response. A frequency-domain approach based on the z-transform was presented in Chapter 2, where an infinite data sequence was converted to an algebraic equation and a DSP system was described compactly by a transfer function; the former enables the frequency spectrum of a signal to be estimated and the latter enables the stability and the frequency response of a DSP system to be assessed.