Timeline for Understanding FFTs for simple Circular Function (sin/cos)
Current License: CC BY-SA 4.0
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| Mar 7, 2022 at 13:20 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Sep 25, 2020 at 11:47 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Sep 25, 2020 at 11:42 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 16, 2020 at 12:00 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 16:49 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 12:10 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 10:53 | comment | added | Jonas Jo | true, I was thinking of visualizing the amplitude. This would only be correct if I'd focus on the positive frequencies only. | |
| Apr 15, 2020 at 10:14 | comment | added | teeeeee | Your PSD is now all good, but I think your magnitude is still not quite right. You need to remove the factor of 2. | |
| Apr 15, 2020 at 10:06 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 9:57 | comment | added | Jonas Jo | those were the missing puzzle pieces for me, I adapted my post with a threshold for the phase and the calculation of the PSD. Thanks for the ongoing support. | |
| Apr 15, 2020 at 9:45 | comment | added | teeeeee | As far as your PSD values, I think you missed a factor of $dt$. In this answer dsp.stackexchange.com/a/32206/38419 you can see that the discrete version of the PSD can be written as $$\frac{1}{N\cdot dt}|\textrm{yfft}\cdot dt|^2$$ where $\textrm{yfft}$ is the raw output from the fft(). Instead, you are plotting $$\frac{|\textrm{yfft}|^2}{N}$$. Add the extra $dt$. Does that fix it? | |
| Apr 15, 2020 at 9:37 | comment | added | teeeeee |
To fix the funny business with the phase, try adding some thresholding on the output of the fft, like so yfft = [0 if abs(yfft_) < 1.0e-10 else yfft_ for yfft_ in yfft]. Add this line directly after you do the fft. This is because the phase angle is calculated using arctan of the real divided by the imaginary component, so if you have numerical noise (inherent in the computer precision) then the division blows up.
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| Apr 15, 2020 at 9:30 | comment | added | Jonas Jo | Thanks for these suggestions on adjustments. Now it works quite well already. Two open points that I see at the moment: 1. The phase value of 2.712 for +3Hz is correct, but why is the Phase signal so distorted in comparison to yours? Is that because of the inaccuracy of Pythons FFT method ? 2. My PSD magnitudes are 10 times too big. | |
| Apr 15, 2020 at 9:15 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 9:10 | vote | accept | Jonas Jo | ||
| Apr 15, 2020 at 9:09 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 8:46 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 8:42 | comment | added | teeeeee |
That should correct all the frequency axis problems. To see the phase, try plotting np.angle(yfft), and you should see a value of 2.712 for the phase of the +3Hz frequency.
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| Apr 15, 2020 at 8:35 | comment | added | teeeeee |
@JonasJo it also looks like you made a mistake in how you define fs. Change fs = tmax / npts to dt = tmax / npts, and then add fs = 1/dt. Finally, I would change the time vector definition to this t = np.linspace(0, tmax-dt, npts) so that you coherently sample the wave, as I mentioned in my answer. Finally, change your frequency definition to this: freq = np.fft.fftfreq(N)*fs
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| Apr 15, 2020 at 8:26 | comment | added | teeeeee |
@JonasJo you need to apply fftshift() around the output of your fft, to make it match with your frequency vector: yfft = np.fft.fftshift(np.fft.fft(y))
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| Apr 15, 2020 at 8:19 | comment | added | Jonas Jo | Hello teeeeee, thanks for your answer. The first link was very helpful. I didn't know that the PSD is the physically correct representation. I'll try to use it in the future. I can understand your answer, but I'm still wondering why my solution, does not show the magnitudes at frequency 3 with Phase 2.7. Is my way of calculating the phase correct? | |
| Apr 15, 2020 at 8:09 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 15, 2020 at 7:37 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 14, 2020 at 22:01 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 14, 2020 at 21:55 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 14, 2020 at 21:49 | history | edited | teeeeee | CC BY-SA 4.0 |
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| Apr 14, 2020 at 21:40 | history | answered | teeeeee | CC BY-SA 4.0 |