Transcription of z-Transforms Chapter 7
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z-Transforms Chapter 7
ECE 2610 Signal and Systems7 1z-TransformsIn the study of discrete-time signal and systems, we have thus farconsidered the time-domain and the frequency domain. The z-domain gives us a third representation. All three domains arerelated to each other. A special feature of the z- transform is that for the signalsand system of interest to us, all of the analysis will be in terms ofratios of polynomials. Working with these polynomials is rela-tively straight of the z- transform Given a finite length signal , the z- transform is definedas( )where the sequence support interval is [0, N], and z is anycomplex number This transformation produces a new representation of denoted Returning to the original sequence (inverse z- transform ) requires finding the coefficient associated with the nth powerof xn[]Xz()xk[]zk k0=N xk[]z1 ()kk0=N ==xn[]Xz()xn[]z1 Chapter7 Definition
The z-Transform and Linear Systems ECE 2610 Signals and Systems 7–4 † To motivate this, consider the input (7.5) † The output is (7.6) † The term in parenthesis is the z-transform of , also known as the system function of the FIR filter † Like was defined in Chapter 6, we define the system
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