What does the weight of the fir filter mean?

What does the weight of the fir filter mean?

Is it multiplied by a certain physical quantity of the sound wave?

Like the Taylor series, does it get closer to the true value as the degree increases?

https://kr.mathworks.com/matlabcentral/fileexchange/159311-kalman-filter-for-active-noise-control

[Umar]

Hi myeongsuk,

The brief answer is that it refers to the coefficients applied to the input signal, bear in mind that each weight in the FIR filter contributes to the filtering process. Please let me know if you have further questions.

[myeongsuk shim]

Thanks for the explanation. I don't understand why the coefficients are multiplied when the signal passes through the filter. Is the x(n) signal decomposed by order n and multiplied by the weight?

[Mathieu NOE]

@myeongsuk shim

we are talking here digital filters

if you need to learn about FIR and IIR digital filters, how they works on signals, there are many ressources available on internet :

digital_filter.pdf (ucdavis.edu)

The Scientist and Engineer's Guide to Digital Signal Processing Introduction to Digital Filters (analog.com) the full guide is available here : The Scientist and Engineer's Guide to Digital Signal Processing (dspguide.com)

and many more

Active noise control use "adaptive" filters , their coefficients are adapted by a tuning algorithm in order to minimize some criterion, usually the mean squared error of the input signal

Introduction to Active Noise Control (ntu.edu.sg)

(PDF) LMS Adaptive Filters for Noise Cancellation: A Review (researchgate.net)

you can also find many books on this topic like :

Introduction to Adaptive and Robust Active Vibration Control | SpringerLink

[Umar]

Hi myeongsuk,

Please see my comments to your questions.

I don't understand why the coefficients are multiplied when the signal passes through the filter.

Each coefficient corresponds to a specific frequency component that the filter is designed to affect. By multiplying the input signal with these coefficients, the filter can selectively attenuate or amplify different frequency components of the signal, shaping its overall frequency response as desired.

Is the x(n) signal decomposed by order n and multiplied by the weight?

Signal decomposition involves breaking down a signal into its components for analysis, while multiplication by weights may be part of other signal processing techniques but is not inherently linked to decomposition by order n.

Please let me know if you have any further questions.

[myeongsuk shim]

It really helped me understand digital filters. thank you!

[Umar]

Hi myeongsuk,

Glad to help out. Please let me know if you accept the answer and have any further questions.