# Sampling frequency after aggregations

I have accelerometer signal, which is preprocessed by the actigraph on-device. Original sampling rate is 32 Hz, but activity count is summed for every minute, so I have a signal with 1 measurement per minute.

For denoising and to analyze long-term dependencies (my data spans several days), especially related to circadian rhythm, I aggregate this data for each hour, taking the mean. After this I have a signal with 1 measurement per hour.

Libraries for analysis of frequency features, e.g. Scipy or TSFEL require sampling rate as a parameter, e.g. for calculating periodogram.

What should be my sampling rate after all this processing?

• 32 Hz, since original measurements were gathered with this frequency?
• 1 Hz, since as a part of very basic preprocessing (and since I don't care about minor movements and analysis of short term effects) a total activity per minute was calculated?
• 1/3600 Hz, since after aggregating by hour I have one measurement per hour?
• it depends on purpose and results and no single answer is totally right or wrong?

## 1 Answer

It depends on which signal you want to do frequency analysis with. If you are doing frequency analysis on the 1/3600 Hz signal, then that is the sample rate the function probably expects. If you are doing frequency analysis on the 1 Hz signal, then use 1 Hz as the sample rate parameter in the function you are using.

• So just to make sure: if I just performed downsampling, i.e. took 1 measurement from each hour, that would be 1/3600 Hz, and if I take mean of measurements for each hour it is also 1/3600 Hz, right? Aug 20, 2021 at 9:22
• Yes that is correct
– Ryan
Aug 20, 2021 at 9:39