How to plot bode diagram of a signal using fft in MATLAB? - matlab

Question

I want to plot bode diagram of the following system both using bode and fft:
%// System info
num=[0 1]; %// Numerator of z-transform of impulse response of system
den=[1 -0.8]; %// Denominator of z-transform of impulse response of system
I used dbode to plot bode method:
figure(6); dbode(num,den,1) %// 1 is sampling time Ts
As I want to do it from fft method, it gets wrong:
Ts=1;
Fs=1/Ts;
L=length(ym);
NFFT = 2^nextpow2(L); %// Next power of 2 from length of ym
H2=fft(ym,NFFT)./fft(u,NFFT);
f=Fs/2*linspace(0,1,NFFT/2+1);
ww=f*2*pi;
figure(7)
semilogx(20*log10(abs(H2(1:NFFT/2+1))))
figure(10)
semilogx((180/pi)*angle(H2(1:NFFT/2+1)))
Bode diagram using bode:
Any idea
Here is my data (u and ym)

Answer 1

I looked at your data and compared it with the theoretical transfer function in the time-domain and it isn't a bad fit if you ignore some of the data:
t = 1:length(u);
num=[0 1]; %// Numerator of z-transform of impulse response of system
den=[1 -0.8]; %// Denominator of z-transform of impulse response of system
H = tf(num,den,1)
[yy,tt,xx] = step(H,max(t));
plot(t-10,ym-2.2,tt,yy)
You'll notice that I have discarded the time values before 10 and shifted the response values down by about 2.2. This gives the following plot (in Octave):
I suggest you do the same thing when taking the FFT:
L = length(ym(t>=10));
NFFT = 2^nextpow2(L);
H2 = fft(ym(t>=10)-2.2,NFFT)./fft(u(t>=10),NFFT);
f=Fs/2*linspace(0,1,NFFT/2+1);ww=f*2*pi;
[mag,ph,w ] = bode(H);
semilogx(ww,20*log10(abs(H2(1:NFFT/2+1))),w,20*log10(abs(mag)))
The DC level of the transfer function is correct, but the poor FFT technique yields too much noise at (relatively) higher frequencies. tfestimate would be a better choice to estimate the transfer based on the measurement data (again remember to pre-process the data the same way as I have just done here). It is part of the Signal Processing Toolbox.