# Issue in finding Power Spectral Density of fitted curve

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Rohan Gupta 2017 年 7 月 4 日

I have a respiration signal which is sinusoidal in shape. I have fitted the curve using Fourier series. Since the fitted curve is in cfit format, I am not able to find it's Power Spectral Density.
Can anyone help me out with this.

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### 採用された回答

dpb 2017 年 7 月 4 日

Evaluate the fit at the desired frequency for however long you have data and pass that result to fft
ADDENDUM: See the comment below for specific, but just use
yhat=resp_f(t);
to get predicted y at times t
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dpb 2017 年 7 月 6 日

If you did a Fourier fit, there's no content in the fitted signal other than that in the specific terms in the fitted equation and they're all known identically.
If you subsequently do actually calculate a PSD by either method, you'll see the peaks at the terms in the fitted model.
The spectrum will, however, not be single spikes at only those frequencies but will be smeared into adjacent frequency bins. These are simply artifacts, however, not actual "real" energy and are due to the windowing and symmetry effects inherent in the computation of a sampled signal.

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### その他の回答 (1 件)

Image Analyst 2017 年 7 月 4 日
Did you pass the signal into pwelch()? (Requires Signal Processing Toolbox.)
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dpb 2017 年 7 月 5 日

But you now already know what the frequency content of the fitted signal is from the series fit anyway????
Still, pwelch isn't enabled to process a cfit object, evaluate the fit and pass that...
t = [1:1:1800]./300;
[resp_f,gof,output] = fit(t',resp_signal,'fourier8');
[pxx2,w2] = pwelch(resp_f(t),[],[],[],Fs);
...

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