Doppler Effect with Pendulum - Understanding Frequency Resolution

[Avi.marchewka@gmail.com]

Hi everyone,
I'm conducting a Doppler effect experiment using Phyphox with a pendulum setup. I have a tone generator (around 500 Hz) attached to a swinging pendulum, and a second phone using Phyphox to measure the Doppler shift. I'm observing frequency variations of a few Hz (around 3 Hz), which seems reasonable.
I'm particularly interested in understanding how Phyphox achieves this frequency resolution. I understand that techniques like FFT, windowing, and peak detection are likely involved. However, I'd appreciate it if someone could provide more details about the specific signal processing steps used by the app.
Specifically, I'm curious about:

1. The window size used for the FFT. How does the window size affect the frequency and time resolution in this context? Is there an optimal window size for this type of experiment?
   
2. Any pre-processing steps applied to the audio signal before the FFT (e.g., filtering, amplification).
   
3. How Phyphox identifies the frequency peak in the FFT output. What peak detection algorithm is used?
   
4. How the Doppler shift is calculated from the measured frequency.
   
5. Are there any specific settings within the Phyphox app that I should be aware of to optimize the frequency resolution and accuracy of the Doppler shift measurements?
   

Any insights into these questions would be greatly appreciated! I'm trying to understand the limitations and capabilities of Phyphox for this type of measurement.
Thanks in advance for your help!

[Jens Noriʇzsɔɥ]

You could find the source of the “Doppler effect” experiment at https://github.com/phyphox/phyphox-exper...er.phyphox and the key analysis function appears to be “periodicity” that is documented at https://phyphox.org/wiki/index.php/Analy...eriodicity (I am not yet entirely sure myself that I fully grasp what the module is doing. It is rather autocorrelation and definitely not FFT.).