# Filter Z Transform Implementation

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LB on 22 Jan 2021
Commented: Star Strider on 22 Jan 2021
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

Star Strider on 22 Jan 2021
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.
##### 2 CommentsShowHide 1 older comment
Star Strider on 22 Jan 2021
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])
.

R2018b

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