# Signal Processing – Filters

Never really have been working with signals before, I first needed a basic fundamental understanding of filters. The following are my notes about low-pass and high-pass filters taking of the youtube video made by ritvikmath.

## Terminology

• low frequency: signal doesn’t change much over time
• high frequency: signal does change a lot over time
• attenuate: reduce intensity of signal

## Low-Pass and High-Pass Filter

### Low-Pass Filter

• Goal: smoothening or denoising
• smooths high frequency areas and passes low frequency areas
• e.g. sweep kernel over signals, which can look as easy as following : [1/n, 1/n, … , 1/n]

## High-Pass Filter

• Goal: edge detection or sharpening
• attenuates low frequency (makes them less extreme as in lowers their amplitude)
• can be as simple as an approximated derivative kernel : [-1,1] (tracks the change, high frequency changes more often and is less attenuated than low frequency, where the derivative approaches to zero)

## But wait that’s just the tip of the iceberg!

After a short read, a whole new world opened up to me with exotic words like Finite Impulse Response (FIR) including moving average filters and Infinite Impulse Response (IIR) in which popular filters such as Butterworth and Chebyshev filter are referenced (Mejia-Mejia et. Al., 2022, p.78). Such a filter can both filter low and high frequency, called band-pass filter. But I think that is a topic for another blog post :).

## References

Mejía-Mejía, E., Allen, J., Budidha, K., El-Hajj, C., Kyriacou, P. A., & Charlton, P. H. (2022). 4—Photoplethysmography signal processing and synthesis. In J. Allen & P. Kyriacou (Eds.), Photoplethysmography (pp. 69–146). Academic Press. https://doi.org/10.1016/B978-0-12-823374-0.00015-3

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