Plot Spectrum reports wrong peak Hz

[RichR]

Using Audacity 2.3.2, I found a bug while attempting to clean up a recorded file. Plot Spectrum indicated a peak of 58 Hz. When I applied a narrow (50.0) Notch Filter at 58 Hz, it made no difference. Turns out the actual peak was at 60 Hz; after I applied the Notch Filter at 60 Hz, Plot Spectrum showed the noise was gone.

Reproducing the bug is very easy...

1. Open a New file (File > New)
2. Generate > Tone...
3. Waveform: Sine, Frequency (Hz): 60, Amplitude (0-1): 0.25, Duration: 1.000s, click OK
4. Analyze > Plot Spectrum...
5. In the Frequency Analysis window (Algorithm: Spectrum, Size: 8192, Function: Rectangular, Axis: Log & make it as large as possible to see detail), place the cursor at the exact peak of the plot. Note the Cursor: value indicates the peak is at 59 Hz, while the Peak: value says 58 Hz (A#1). (But you know you generated a 60 Hz tone.)

If you wish, experiment with the Notch Filter to further examine the problem.

[steve]

5. In the Frequency Analysis window (Algorithm: Spectrum, Size: 8192, Function: Rectangular, Axis: Log & make it as large as possible to see detail), place the cursor at the exact peak of the plot. Note the Cursor: value indicates the peak is at 59 Hz, while the Peak: value says 58 Hz (A#1). (But you know you generated a 60 Hz tone.)

As shown below, I'm seeing the peak reported as 61 Hz, but you are using a different window function (I'm using the default "Hann" window as you can see)

Screenshot_2019-11-15_17-30-55.png (47.33 KiB) Viewed 266 times

Plot Spectrum uses FFT analysis, which gives an approximation of the frequency spectrum. A larger window size gives a closer approximation on frequency values:

Screenshot_2019-11-15_17-36-01_2.png (46.49 KiB) Viewed 266 times

It's not a bug, it's a limitation of FFT analysis that the smaller the window, the less precise the approximation is.

[RichR]

It's not a bug, it's a limitation of FFT analysis that the smaller the window, the less precise the approximation is.

Hmm... knowing nothing about FFT analysis, I had supposed the smaller window would result in a more precise approximation.

However, I found using the 32768 window gave the proper results, no matter what tone I chose for my tests.

Good to know.

Thanks!

[steve]

Hmm... knowing nothing about FFT analysis,

There is a bit of information about it, in not too technical language, here: https://manual.audacityteam.org/man/plot_spectrum.html