Title:
Z-Transform In MATLAB
Objective:
Z-Transform
Inverse Z-Transform
Pole / Zero plots
Pratial Fraction
Region of Convergence
Z-Transform convolution theorm
Software/Tool:
MATLAB Software
Procedure:
Z-Transform:
The Z-transform converts a discrete-time signal, which is a sequence of real or
complex numbers, into a complex frequency-domain representation. It can be
considered as a discrete-time equivalent of the Laplace transform.
Inverse Z-Transform:
x(z)=N(Z)/D(Z) Now, if we go on dividing the numerator by denominator, then we
will get a series as shown below. X(z)=x(0)+x(1)Z−1+x(2)Z−2+. The sequence
represents the series of inverse Z-transform of the given signal forn≥0 and the
above system is causal.
Tasks:
convolve the following:
u[n] ; (0.5)n u[n] n=0:6
Z-Transform:
an :
n3:
-an:
cos (wn):
sin (wn):
an cos (wn):
an sin (wn):
Inverse Z-Ttansform:
(z^2+2*z) / (z^2+0.2)
(z^2+2*z) / (z^2+0.2)
Pole / Zero Plot:
1 / ( (1-0.9*z^-1)^2*(1+0.9*z^-1) )
(z^3+1) / (z^3-z^2-z-2)
1 / ( (z-0.5)*(z-0.5) )
Conclusion/Result:
In this lab, we studied Z-Transform using different examples.
we have performed different Z-Transform codes with plotting of poles / zeros by
solving equations using partial fraction, also region of convergence graph.
