Frequency response using input and output parameters only.

Can we make a frequency response of a system, given input signal, output signal, bandwidth and Gain.

Answer 1

[Mathieu NOE]

hi

you can make a FRF plot of an unknown system from input / output data with tfestimate (requires the Signal Processing Toolbox)

if you don't have the Signal Processing Toolbox , here's a demo with a equivalent code

the input / output data is attached

hope it helps

data = load('beam_experiment.mat');
x = transpose(data.x); %input
y = transpose(data.y); %output
fs = data.fs;   % sampling frequency

NFFT = 2048;
NOVERLAP = round(0.75*NFFT);  % 75 percent overlap

%% solution 1 with tfestimate (requires Signal Processing Tbx)
% [Txy,F] = tfestimate(x,y,hanning(NFFT),NOVERLAP,NFFT,fs);

%% alternative with supplied function 
[Txy,Cxy,F] = mytfe_and_coh(x,y,NFFT,fs,hanning(NFFT),NOVERLAP); 
% Txy = transfer function (complex), Cxy = coherence, F = freq vector

% Bode plots
figure(1),
subplot(3,1,1),plot(F,20*log10(abs(Txy)));
ylabel('Mag (dB)');
subplot(3,1,2),plot(F,180/pi*(angle(Txy)));
ylabel('Phase (°)');
subplot(3,1,3),plot(F,Cxy);
xlabel('Frequency (Hz)');
ylabel('Coh');

%%% damping ratioes for modes
N = 2 ; % number of (dominant) modes to identify
[fn,dr] = modalfit(Txy,F,fs,N,'FitMethod','pp');
T = table((1:N)',fn,dr,'VariableNames',{'Mode','Frequency','Damping'})


%%%%%%%%%%%%%%%%%%%%%%%
function [Txy,Cxy,f] = mytfe_and_coh(x,y,nfft,Fs,window,noverlap)
% Transfer Function  and Coherence Estimate 
    
% compute PSD and CSD
window = window(:);
n = length(x);		% Number of data points
nwind = length(window); % length of window
if n < nwind    % zero-pad x , y if length is less than the window length
    x(nwind)=0;
    y(nwind)=0;  
    n=nwind;
end
x = x(:);		% Make sure x is a column vector
y = y(:);		% Make sure y is a column vector
k = fix((n-noverlap)/(nwind-noverlap));	% Number of windows
					% (k = fix(n/nwind) for noverlap=0)
index = 1:nwind;

Pxx = zeros(nfft,1); 
Pyy = zeros(nfft,1); 
Pxy = zeros(nfft,1); 

for i=1:k
    xw = window.*x(index);
    yw = window.*y(index);
    index = index + (nwind - noverlap);
    
    Xx = fft(xw,nfft);
    Yy = fft(yw,nfft);
    Xx2 = abs(Xx).^2;
    Yy2 = abs(Yy).^2;
    Xy2 = Yy.*conj(Xx);
    Pxx = Pxx + Xx2;
    Pyy = Pyy + Yy2;
    Pxy = Pxy + Xy2;
    
end

% Select first half
if ~any(any(imag([x y])~=0))   % if x and y are not complex
    if rem(nfft,2)    % nfft odd
        select = [1:(nfft+1)/2];
    else
        select = [1:nfft/2+1];   % include DC AND Nyquist
    end

    Pxx = Pxx(select);
    Pyy = Pyy(select);
    Pxy = Pxy(select);
    
else
    select = 1:nfft;
end
Txy = Pxy ./ Pxx;                   % transfer function estimate 
Cxy = (abs(Pxy).^2)./(Pxx.*Pyy);    % coherence function estimate 

f = (select - 1)'*Fs/nfft;

end

[Mathieu NOE]

Hello

Problem solved ?

Answer 2

[Star Strider]

What data are you starting with, and what do you want to do with them?

If you want to identify the system, see the documentation for iddata, idfrd, invfreqz, or similar functions.

Otherwise, if you have the time-domain data, the fft function can calculate the Fourier transform of them.

The bandwidth and gain may not be necessary as inputs, however could help characterise it.