Filter Z Transform Implementation

Hello,

I would like to know how to implement a filter in Matlab in the Z transform like : H(z)= -1/2 - z^(-1) - 1/2*z^-2

Im trying to get the impulse response with impz but have since failed in doing so.

Thank you

Answer 1

[Star Strider]

The easiest way is to let the Control System Toolbox do the initial analysis:

z = tf('z');                                                    % Use Control System Toolbox Functions
H = tf( -1/2 - z^(-1) - 1/2*z^-2, 'Variable','z^-1')

filt_a = H.Numerator{:};
filt_b = H.Denominator{:};

figure
freqz(filt_b, filt_a)

figure
impulse(H)

figure
impz(filt_b, filt_a)

producing:

H =
 
  -0.5 z^3 - z^2 - 0.5 z
  ----------------------
           z^3
 
Sample time: unspecified
Discrete-time transfer function.

and the plots.

[LB]

Is it always freqz(den,num) or freqz(num,den)?

Im confused my teachers use impz freqz...(num,den)

EDIT: would something like num = [-1/2 -1 -1/2], den=1, h=impz(num,den), impz(h) work?

Thank you!

[Star Strider]

I always used:

freqz(num, den)

that appears to be correct according to the freqz documentation.

‘... would something like num = [-1/2 -1 -1/2], den=1, h=impz(num,den), impz(h) work?’

Not exactly, although this would:

num = [-1/2 -1 -1/2]; 
den = 1;

[h,t] = impz(num,den);

figure
stem(t, h, 'filled', 'LineWidth',2)
axis([0 max(t)+0.5  -1.5 1.5])

.