Student summary z transform ECE438F09 - Rhea

The Z-Transform

The z-transform converts a discrete-time signal into a complex frequency domain representation.

• $ X(z) = \sum_{n=-\infty}^\infty (x[n]z^{-n}) $

Some Properties:

Linearity:

• $ ax1[n]+bx2[n] = aX1(z)+bX2(z) $

Time-Shifting:

• $ x[n-k] = z^{-k}X(z) $

Scaling in Z domain:

• $ a^{n}Y(z) = X(a^{-1}Z) $

Time Reversal:

• $ x[-n] = X(z^{-1}) $

Convolution:

• x1[n]* x2[n] = X1(z)X2(z)