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Problem with polyfit and polyval

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Problem with polyfit and polyval

Timothy asked: matlab , signal , signal processing

Troubleshoot issues with MATLABs polyfit and polyval functions. Learn how to resolve common problems, improve your curve fitting accuracy, and get reliable res

Expert Answer

Profile picture of Kshitij Singh Kshitij Singh answered . 2025-07-03 22:19:50

It took me a few minutes to come up with this purely signal processing approach, so no curve fitting required. Experiment with the numerator and denominator orders of the transfer function to get the result you want. (Another option would be the firls function, and there are other empirical methods to consider depending on what you want to do. There is also the entire System Identification Toolbox! You are doing system identification here.)
 
It should give you everything you want:
 
D = load('Philippe Amp.mat');
Freq = D.Amp(:,1);                                              % Hz Frequency Vector
Vi = D.Amp(:,3);
Vo = D.Amp(:,4);
H = Vo./Vi;                                                     % Amplitude Transfer Function
Phase = D.Amp(:,4);
W = Freq/max(Freq)*pi;                                          % Radian Frequency Vector

figure(1)                                                       % Look At The Data
subplot(2,1,1)
plot(Freq,Vi,  Freq,Vo)
grid
subplot(2,1,2)
plot(Freq, Phase)
grid

figure(2)
subplot(2,1,1)
plot(Freq, 20*log10(H))
ylabel('Magnitude (dB)')
grid
axis([xlim    -40  0])
subplot(2,1,2)
plot(Freq, Phase)
ylabel('Phase (degrees)')
grid

Hc = H .* exp(1i*pi*Phase/180);                                 % Create Complex Frequency Response
Hc(1) = interp1(Freq(2:end),Hc(2:end), 0, 'spline','extrap');   % Replace Initial ‘NaN’ Value

OrdNum = 3;
OrdDen = 5;
[b,a] = invfreqz(Hc, W, OrdNum, OrdDen);                        % Transfer Function Coefficients

figure(3)
freqz(b, a, 4096)                                               % Bode Plot

figure(4)
impz(b, a)                                                      % Impulse Response


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