# Removing low frequency vibrations from measured signal

Suppose I have two sensors $s_1$ and $s_2$. $s_1$ measures the desired heart signal (with most of the frequency content below 100 Hz), and the other is a reference sensor picking mainly background noise.

Due to the pumping of the blood in the heart, there is also low frequency vibrations, mainly below 10 Hz that contaminates both sensors. The sensors are spatially separated, making direct cancellation unfeasible.

The figure below shows the frequency content of both sensors ($s_1$ is blue and $s_2$ is red), following discrete Fourier Transform. The visible peak is the 50 Hz mains hum.

Nonlinear denoising is effective in removing mains hum without compromising the signal. However, it seems to be ineffective in removing the low frequency vibrations. The figure below shows the effect of applying it to $s_1$

My question is how can these vibrations be removed from $s_1$, without causing too much distortion to the desired signal?

• I hope you can use simple adaptive filters such as LMS or RLS types in a noise cancelling configuration. – Fat32 May 9 '16 at 15:46
• What is the frequency range of interest? Is it a range or a single frequency you are interested in? – Amal May 9 '16 at 20:03
• @user3288586 it is a range, 2-10 Hz. – Abbas May 9 '16 at 20:07
• Looks like this is the range you want to remove. You can use a bandstop filter. – Amal May 9 '16 at 20:08
• @user3288586 yes this is the range in which vibrations contaminate the desired signal. Consequently, using a bandstop filter will distort the signal. – Abbas May 9 '16 at 20:13