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Liang Kar Yan on 10 Dec 2021
Commented: Liang Kar Yan on 14 Dec 2021
Accepted Answer: Mathieu NOE
- TF.m
I have 3 individual files which are Magnitude(dB), Phase(degrees) and Frequency(Hz) in excel. I need to find the transfer function with these data. After getting the transfer function, I need to plot back the graph (magnitude and phase) from transfer function to compare with my data.
I wish to get something like the picture attached below.
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Mathieu NOE on 13 Dec 2021
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hello
can you also provide the 3 exel files ?
Liang Kar Yan on 13 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1884575
- Frequency.xlsx
- Magnitude.xlsx
- Phase.xlsx
Hi sure,
Thank you so much.
Star Strider on 13 Dec 2021
Direct link to this comment
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Open in MATLAB Online
Something is definitely wrong with these data!
They do not describe a frequency-response function —
Freq = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/833095/Frequency.xlsx')
Freq = 2001×1
100.0000 100.1000 100.2000 100.3000 100.4000 100.5000 100.6000 100.7000 100.8000 100.9000
Magn = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/833100/Magnitude.xlsx')
Magn = 2001×1
-43.9413 -43.8619 -43.7825 -43.7031 -43.6236 -43.5442 -43.4648 -43.3853 -43.3059 -43.2265
Phse = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/833105/Phase.xlsx')
Phse = 2001×1
111.3686 105.0197 98.6691 92.3168 85.9627 79.6068 73.2493 66.8899 60.5289 54.1661
cplxv = Magn .* exp(1j*deg2rad(Phse))
cplxv =
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figure
subplot(2,1,1)
plot(Freq, Magn)
grid
subplot(2,1,2)
plot(Freq, Phse)
grid
frd = idfrd(cplxv, Freq, 1/(2*Freq(end)))
frd =IDFRD model.Contains Frequency Response Data for 1 output(s) and 1 input(s).Response data is available at 2001 frequency points, ranging from 100 rad/s to 300 rad/s. Sample time: 0.0016667 secondsStatus: Created by direct construction or transformation. Not estimated.
figure
plot(Freq, imag(cplxv))
NrPoles = nnz(islocalmax(imag(cplxv)))
NrPoles = 44
sys_tf = tfest(frd, 2, 1)
sys_tf = -19.56 s - 3578 ------------------------- s^2 + 0.9124 s + 1.296e04 Continuous-time identified transfer function.Parameterization: Number of poles: 2 Number of zeros: 1 Number of free coefficients: 4 Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties.Status: Estimated using TFEST on frequency response data "frd".Fit to estimation data: 2.943% FPE: 188.8, MSE: 188.1
figure
compare(frd, sys_tf)
grid
.
Mathieu NOE on 14 Dec 2021
Direct link to this comment
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hello @Star Strider
I believe Magn is given in dB (like in the plot)
so first think is to convert back to linear magnitude
Magn = 10.^(Magn/20) , and then
cplxv = Magn .* exp(1j*deg2rad(Phse))
Liang Kar Yan on 14 Dec 2021
Direct link to this comment
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Hi @Star Strider, thank you for your help.
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Accepted Answer
Mathieu NOE on 14 Dec 2021
Open in MATLAB Online
hello
I tried a few options , IIR or FIR filters fit.
As the phase plot shows , there is a quite significant phase roll rate, idicating the presence of a huge delay in the system.
I assumed a sampling rate of Fs = 1000 hz and found out that more or less we can fit either a FIR or a IIr high pass filter in series with almost 200 samples of delay (hudge !!)
maybe there are more powerful tools then the simple invfreqz (not giving any good results here) or the manual fit I am doing here
FIR fit plot :
IIR fit plot :
clc
clearvars
Freq = readmatrix('Frequency.xlsx');
Magn_dB = readmatrix('Magnitude.xlsx');
Phse = readmatrix('Phase.xlsx');
figure(1)
subplot(211),plot(Freq,Magn_dB);
subplot(212),plot(Freq,Phse);
Magn = 10.^(Magn_dB/20) ;
%% high pass filter model (IIR)
Fs = 1000; % ? to be confirmed
N = 8; % filter order
dc_gain = Magn(end); % asymptotic value
[val,ind] = min(abs(Magn_dB - Magn_dB(end) + 5)); % - 5dB (vs dc_gain) cut off frequency index search
fc = Freq(ind); % - 5dB (vs dc_gain) cut off frequency
[b,a] = butter(N,2*fc/Fs,'high');
b = b*dc_gain; % apply dc gain on numerator
[g,p] = dbode(b,a,1/Fs,2*pi*Freq);
% adding delay due to sampling
nd = 200; % delay (samples)
rpd = -360*nd*Freq/Fs;
p = p+rpd; % adding filter phase to samples delay phase
p = mod(p,360);
p = p -180; % polarity correction
figure(1)
subplot(211),plot(Freq,Magn_dB,Freq,20*log10(g));
title('IIR model fit')
ylabel('Modulus (dB)');
subplot(212),plot(Freq,Phse,Freq,p);
xlabel('Frequency (Hz)');
ylabel('Phase (°)');% return
%% high pass filter model (FIR)
Fs = 1000; % ? to be confirmed
N = 20;
dc_gain = Magn(end); % asymptotic value
[val,ind] = min(abs(Magn_dB - Magn_dB(end) + 3)); % - 3dB (vs dc_gain) cut off frequency index search
fc = Freq(ind); % - 3dB (vs dc_gain) cut off frequency
[b,a] = fir1(N,2*fc/Fs,'high');
b = b*dc_gain; % apply dc gain on numerator
[g,p] = dbode(b,a,1/Fs,2*pi*Freq);
% adding delay due to sampling
Fs = 1000; % ? to be confirmed
nd = 200; % delay (samples)
rpd = -360*nd*Freq/Fs;
p = p+rpd; % adding filter phase to samples delay phase
p = mod(p,360);
p = p -180; % polarity correction
figure(2)
subplot(211),plot(Freq,Magn_dB,Freq,20*log10(g));
title('FIR model fit')
ylabel('Modulus (dB)');
subplot(212),plot(Freq,Phse,Freq,p);
xlabel('Frequency (Hz)');
ylabel('Phase (°)');
%% Id with invfreqz (FIR)
h = Magn .* exp(1j*180/pi*(Phse));
nb = 40+nd;
na = 1;
iter = 1000;
[bb,aa] = invfreqz(h,pi*Freq/Fs,nb,na,[],iter); % stable approximation to system
[g,p] = dbode(bb,aa,1/Fs,2*pi*Freq);
p = mod(p,360);
figure(3)
subplot(211),plot(Freq,Magn_dB,Freq,20*log10(g));
subplot(212),plot(Freq,Phse,Freq,p);
10 Comments Show 8 older commentsHide 8 older comments
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Liang Kar Yan on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1885870
Hi @Mathieu NOE, thank you for your help. Is there any method to get the transfer function equation from the graph?
Mathieu NOE on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886055
Open in MATLAB Online
hello again
this is a method using ifft to fit a FIR model to a given complex FRF- it works on some examples like the one below
clc
clearvars
%
Fs = 1e3;
Freq = linspace(0,Fs/2,100);
b = fir1(48,[0.3 0.5]); % Window-based FIR filter design
frf = freqz(b,1,Freq,Fs);
if mod(length(frf),2)==0 % iseven
frf_sym = conj(frf(end:-1:2));
else
frf_sym = conj(frf(end-1:-1:2));
end
fir = real(ifft([frf frf_sym]));
frfid = freqz(fir,1,Freq,Fs);
figure(1)
subplot(211),plot(Freq,20*log10(abs(frf)),Freq,20*log10(abs(frfid)));
legend('FIR input model','identified FIR model');
subplot(212),plot(Freq,180/pi*angle(frf),Freq,180/pi*angle(frfid));
legend('FIR input model','identified FIR model');
but when I try to use it on your data , it fails ... ugh !
clc
clearvars
Fs = 1e3;
Freq = readmatrix('Frequency.xlsx');
Magn_dB = readmatrix('Magnitude.xlsx');
Phse = readmatrix('Phase.xlsx');
figure(1)
subplot(211),plot(Freq,Magn_dB);
subplot(212),plot(Freq,Phse);
Magn = 10.^(Magn_dB/20) ;
frf = Magn .* exp(1j*pi/180*(Phse)); % FRF complex
if mod(length(frf),2)==0 % iseven
frf_sym = conj(frf(end:-1:2));
else
frf_sym = conj(frf(end-1:-1:2));
end
fir = real(ifft([frf; frf_sym]));
frfid = freqz(fir,1,Freq,Fs);
figure(1)
subplot(211),plot(Freq,20*log10(abs(frf)),Freq,20*log10(abs(frfid)));
subplot(212),plot(Freq,180/pi*angle(frf),Freq,180/pi*angle(frfid));
Mathieu NOE on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886070
I think we could get a better result if your data was available on broader frequency range (from 0 to Fs/2) is Fs = sampling rate
Liang Kar Yan on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886080
Hi, thank you so much for your help. The frequency is actually at 100GHz to 300GHz.
Mathieu NOE on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886105
are you measuring an analog or digital filter / circuit ?
seems very high frequency range for anything digital ....
Mathieu NOE on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886115
Open in MATLAB Online
converting my code from 'Hz' to GHz by factor 10^9 is just making a new scale factor on the frequency axis , but not any impact on the FIR model output by itself
clc
clearvars
Freq = readmatrix('Frequency.xlsx'); % in Hz
Freq = Freq*1e9;% now in GHz
Fs = 2.56*max(Freq);
Magn_dB = readmatrix('Magnitude.xlsx');
Phse = readmatrix('Phase.xlsx');
figure(1)
subplot(211),plot(Freq,Magn_dB);
subplot(212),plot(Freq,Phse);
Magn = 10.^(Magn_dB/20) ;
frf = Magn .* exp(1j*pi/180*(Phse)); % FRF complex
if mod(length(frf),2)==0 % iseven
frf_sym = conj(frf(end:-1:2));
else
frf_sym = conj(frf(end-1:-1:2));
end
fir = real(ifft([frf; frf_sym]));
% fir = fir(1:end/4);
frfid = freqz(fir,1,Freq,Fs);
figure(1)
subplot(211),plot(Freq,20*log10(abs(frf)),Freq,20*log10(abs(frfid)));
subplot(212),plot(Freq,180/pi*angle(frf),Freq,180/pi*angle(frfid));
Liang Kar Yan on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886135
I'm actually designing a terahertz waveguide at 100GHz to 300GHz and want to observe the s parameters (for this data set is actually the s21 graph).
Liang Kar Yan on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886145
I think the first code is what I want and I manage to get the transfer function as well, thank you so much.
Mathieu NOE on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886195
this is maybe something for you
but beyong my limited time possibilities right now
all the best for the future
Liang Kar Yan on 14 Dec 2021
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1607890-how-can-i-find-the-transfer-function-having-magnitude-db-phase-degree-and-frequency-hz#comment_1886270
Thanks for the useful information.
Thank you.
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