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My aim is to find the optimal cut off frequency for a low pass filter for a normal walking activity. Based on accelerometer data (x y z axis, of a wearable watch), I compute the FFT for each axis and finally the magnitude out of these three axis.

When I plot the results in frequency domain, I usually get peaks around 5 HZ and 10-11 HZ for walking. Usually the 5HZ amplitude will be higher and the 10 HZ peak slightly lower. Occasionally the 10HZ peak will be higher but usually it's the other way around. Which cut off frequency for the low pass filter shall I chose then? Is it slightly above 5HZ (such as 6-7 HZ) or above 10-11HZ (such as 12-13HZ)? Do these cut off frequencies sound plausible for walking?

Thank you very much

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    $\begingroup$ Without knowing your specific application, we cannot say much about the optimal cutoff frequency but as a general rule of thumb you can choose it as slightly higher than your highest frequency component so around 12Hz. $\endgroup$ Apr 22, 2023 at 9:00
  • $\begingroup$ Thank you for your response. It is for walking vs non walking recognition. The 5HZ has a slightly higher amplitude than 10-11HZ however (when recording a walking activity). Does it mean that 5HZ is the highest frequeny component? Therefore a cut off frequency at around 6-7 HZ would be preferable? Thank you $\endgroup$ Apr 22, 2023 at 9:12

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Choosing the right filter typically involves a trade off. It often depends on

  1. What are the spectral properties of the signal you want to keep
  2. What are the spectral properties of the noise you want to get rid off
  3. What particular properties is your algorithm sensitive to

So there is no "one size fits all" answer to your question. It really depends on how your detection algorithm works.

If that's difficult to determine you can try a "trial and error" approach: Build a test corpus of representative signals with known correct answers, try a few different filter designs and measure which one has the highest correct detection rate.

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