بدست آوردن پاسخ فرکانسی تابع همراه با کد متلب Frequency response function

Systems respond differently to inputs of different frequencies. Some systems may amplify components of certain frequencies, and attenuate components of other frequencies. The way that the system output is related to the system input for different frequencies is called the frequency response of the system.

The frequency response is the relationship between the system input and output in the Fourier Domain.

In this system, X(jω) is the system input, Y(jω) is the system output, and H(jω) is the frequency response. We can define the relationship between these functions as:

at the follow the codes for Matlab would show the FRF in an example

clear all
A1=20; A2=30; f1=5; f2=15; wn1=2*pi*f1; wn2=2*pi*f2;
zeta1=0.02; zeta2=0.01;
wd1=sqrt(1-zeta1^2)*wn1; wd2=sqrt(1-zeta2^2)*wn2;
fs=100; T1=10; t1=[0:1/fs:T1-1/fs]; h=(A1/wd1)*exp(-zeta1*wn1*t1).*sin(wd1*t1)+(A2/wd2)*exp(-zeta2*wn2*t1).*sin(wd2*t1);

T= 2000; % T=10000;

randn('state',0);
x=randn(1,T*fs);
y=filter(h,1,x)/fs; % scaled appropriately
Tr=4; N=Tr*fs; % Tr=20;

[Sxx, ~]=cpsd(x,x, hanning(N),N/2, N, fs, 'twosided');
[Syy, f]=cpsd(y,y, hanning(N),N/2, N, fs, 'twosided');

H=fft(h)/fs; % scaled appropriately.

f1=fs*(0:length(H)-1)/length(H);

figure (1)
plot(f,10*log10(fs*Sxx), f, zeros(size(f)), 'r:')

xlabel('Frequency (Hz)')

ylabel('Estimate of \itS x x\rm(\itf\rm) (dB)')

axis([0 30 -10 10])

figure(2)

plot(f,10*log10(Syy),f1,10*log10(abs(H).^2/fs), 'r:')

xlabel('Frequency (Hz)')

ylabel('Estimate of \itS y y\rm(\itf\rm) (dB)')

axis([0 30 -100 -20])

figure(3)

plot(f,10*log10(abs(Sxy)),f1,10*log10(abs(H)/fs), 'r:')

xlabel('Frequency (Hz)')

ylabel('Estimate of |\itS x y\rm(\itf\rm)| (dB)')

axis([0 30 -60 -20])

figure(4)

plot(f,unwrap(angle(Sxy)),f1,unwrap(angle(H)), 'r:')

xlabel('Frequency (Hz)')

ylabel('Estimate of arg\itS x y\rm(\itf\rm))(rad)')

axis([0 30 -3.5 0])