8_The z-Transform(z变换).pdf.pdf

8 The z-Transform 8.1 Introduction 8.2 Properties of the z-Transform Linearity • Translation • Convolution • Multiplication by an • Time Reversal Richard C. Dorf 8.3 Unilateral z-Transform Time Advance • Initial Signal Value • Final Value University of California, Davis 8.4 z-Transform Inversion Zhen Wan Method 1 • Method 2 • Inverse Transform Formula (Method 2) University of California, Davis 8.5 Sampled Data 8.1 Introduction Discrete-time signals can be represented as sequences of numbers. Thus, if x is a discrete-time signal, its values can, in general, be indexed by n as follows: x = {…, x (–2), x (–1), x (0), x (1), x (2), …, x (n), …} In order to work within a transform domain for discrete-time signals, we define the z-transform as follows. The z-transform of the sequence x in the previous equation is • Z {x (n )} = X (z ) = Â x (n)z -n n= -• in which the variable z can be interpreted as being either a time-position marker or a complex-valued variable, and the script Z is the z-transform operator. If the former interpretation is employed, the number multiplying the marker z –n is identified as being the nth element of the x sequence, i.e., x(n). It will be generally beneficial to take z to be