z-tranforms and Convolution in Matlab
Find z-transform in Matlab.
Example:
Find the z-trasform of the sequence (0.5)^n.
syms z n %Declare symbolic variables z and n
f = (0.5).^n; %Define the time sequence
F=ztrans(f) %z-transform
pretty(F);
Find inverse z-transform in Matlab.
Example: Find the inverse z-transform of
syms z n %Declare symbolic variables z and n
F= z/(z-0.5)
f=iztrans(F)
pretty(f);
Exercises:
1. Do problem 2c and 2d from homework of week 5 in Matlab.
(c) and express it in positive powers of z. When computing the value of trigonometric functions, keep in mind that the arguments are always in radians and not in degrees.
and express it in positive powers of z
2. Do problem 3a from homework of week 5 in Matlab.
(a) x(z)= ((2z-0.5))/((Z+0.5) )
then use the z-transform tables. Having found the inverse z-transform, determine its numerical value at n = 2.
Hint: Use the algebraic identity (a±b )/((c) )= a/c± b/c to bring the expression into a form where you can use the tables. Note that if the inverse z-transform of x(z) is x(n), then the inverse z-transform of z^(-k) x(z) is x(n-k),i.e,replace n by (n-k) in the inverse transform since z^(-k) is a delay by k samples.