frequency obtained by cftool is 10 times less than what I should get

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Kunal Tiwari 2017-5-14

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评论： Kunal Tiwari 2017-5-15

Hi everyone, I am using fourier series for one of my application. I was getting wrong result, so I decided to check the fit(t,variable,'fourier1') for small application. I used the following code to generate a cos wave

%%Angular Frequency
    omega=0.65;
   %%Time specifications:
   Fs = 10;                   % samples per second
   dt = 1/Fs;                   % seconds per sample
   StopTime =200*omega/pi;             % seconds
   t = (0:dt:StopTime-dt)';     % seconds
   %%Sine wave:
    x = cos(omega*t);
   % Plot the signal versus time:
   figure;
   plot(t,x);

I used this cos wave in cftool and fit function. both gave me results as in figure.

as you can see, in result I got w=omega=0.065 whereas The original signal was having angular frequency as 0.65;

I have tried this for other frequency too and result is always 10 times less. What am i doing wrong ?

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David Goodmanson 2017-5-15

Hi Kunal, I don't have access to cftool but this gives the impression that some part of the calculation is not getting the message that your time array has spacing of 1e-1. If it were assumed instead that the spacing is 1, then the calculated omega is down by a factor of 10. If you change Fs to 20, does the answer change by that same factor?

Kunal Tiwari 2017-5-15

@David, You nailed it. Changing Fs to 20 made the w reduce by half. I changed Fs to 1 and I got expected result. I was making the mistake of letting matlab assume the sampling frequency. Thanks.

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Answer 1

John D'Errico 2017-5-14

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Decent starting values are critical to finding a good estimate. If you provide no starting values at all, then you get an arbitrary result, often something that will not make you happy.

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Kunal Tiwari 2017-5-14

But does that mean matlab does not use traditional fourier series formulas ?

Actually my application involves equating the coefficients (a0,a1,b1) for getting estimations. So do you think it's better to try and implement these formulas over trying to use fit function ?

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