Why Does My Z-Transform Bode Plot Show Incorrect Amplitude for a Sine Wave?

[bmalp]

Hi,

I try to visualize a sine wave, z-transformed in a Bode plot. The frequency shows up correctly, but the amplitude is way off - why?

Thanks for your comments.
Bmalp



function zdemo

format compact
syms w Ts n z phi t

Ts = 1
w = 0.1
phi = 0

vz = simplify(ztrans(sin(w*n*Ts+phi))) % correct

if 0 % method 1
[num,den] = numden(simplify(vz));
num = collect(num,'z')
den = collect(den,'z')
num1 = sym2poly(num)
den1 = sym2poly(den)
[h,w] = freqz(num1,den1,512,'whole');
else % method 2
fs = 1;
f = linspace(0,fs,256);
w = 2*pi*f;
ss = sqrt(-1)*w;
Z = exp(ss/fs);
h = double(subs(vz,z,Z));
end
plot(w,abs(h)) % amplitude way too big

 

[Mesmer]

Why don't you try this site http://www.kluid.com/". It's pretty much dedicated to MATLAB :)

 

[tacman]

Hello Bmalp,

Thank you for sharing your code and question. It seems like you are on the right track with your z-transform and Bode plot. However, there are a few things that could be causing the incorrect amplitude in your plot.

Firstly, make sure that your frequency w is in the correct units. In your code, you have set w = 0.1, but it is not clear what unit this is in. If you are trying to plot a sine wave with a frequency of 0.1 Hz, then w should be set to w = 2*pi*0.1 = 0.2. This could be one reason why your amplitude is off.

Secondly, check that your time step Ts is correct. In your code, you have set Ts = 1, which means that your sampling frequency is 1 Hz. If you are trying to plot a sine wave with a frequency of 0.1 Hz, then your sampling frequency should be at least 2*0.1 = 0.2 Hz. Try increasing your sampling frequency and see if that improves the amplitude in your plot.

Lastly, it is important to note that the z-transform and Bode plot are not the same as a Fourier transform and frequency plot. The z-transform is a discrete-time equivalent of the Laplace transform, and the Bode plot is used to visualize the frequency response of a system, which is not the same as the frequency content of a signal. So, while your code may give you a rough idea of the frequency response of your system, it may not accurately represent the amplitude of your sine wave.

I hope this helps and gives you some things to consider as you continue to work on your code. Good luck!