Design High-pass filter with very low cut-off frequency

Hello everybody!

I need your help. My first question is: is there some min value of normalized cut-off frequency for high-pass filter?

After integration some data (velocity), I got new data (displacement) with noise with low frequency (less than 128 Hz). My sample frequency is 256 kHz. So, I want to remove this noise by designing FIR highpass filter in Signal Processing Toolbox. The signal, that I am interested in, starts from 9 kHZ (0.07 normalized frequency). So, I tried different variants of choices F_stop and F_pass, that were < 9kHz. But the result of all my attempts is not satisfied. To illustrate my problem I'm attaching some pictures. First picture is the fft of data (displacement) before applying any highness filter. You can see the pick closed to 0.

The second is after applying high pass filter with F_stop = 2 kHz (0.0156 normalized frequency), F_pass = 7 kHz (0.0547 normalized frequency), as an example.

And there is some range of frequencies where the magnitude of the fft of data is too high (in red circle).

Answer 1

[Brandon Eidson]

Hey Svetlana, there is no theoretical limitation to where a high-pass filter's cut-off frequency can be. If you have not already, I suggest plotting the magnitude response of your filter to verify it has the characteristics you expect. A function like "fvtool" will help you analyze the filter you created (documentation linked to below).

https://www.mathworks.com/help/signal/ref/fvtool.html

If the magnitude response is what you expect and, after applying it, you are still getting unexpected results, I suggest you read through the "Practical Introduction to Digital Filtering" documentation linked to below. It will describe how to account for issues like delay and transients that affect a filter's impact (remember, a magnitude response only analyzes the filter's steady-state response).

https://www.mathworks.com/help/signal/examples/practical-introduction-to-digital-filtering.html