Stupid question about FIR filters

[GertDalPozzo]

Hi All,
is there a relationship (a simple formula) between FIR filter order (number of taps) and passband width?
Because I know that if the passband is narrow I need an higher number of taps, but I don't know if this relationship is linear or if there is a way to determine at least the minimum order of the filter for a given bandwidth.

Thanks All!

Gert

 

[Kral]

GertDalPozzo,
GertDalPozzo,
See the following paper:
"An Algebraic Approach to the Estimation of the
Order of FIR Filters From Complete and Partial
Magnitude and Phase Specifications" by Anthony G. Constantinides, Fellow, IEEE, and Wen Min Li.
.
The article appeared in the Vol 55 No 4, April 2007 of the IEEE Transactions on Signal Processing.
.
The article is free to IEEE members. Any decent college or university library can obtain a copy. I can't send you a copy because that would violated copyright laws.
.
The relationship between filter characteristics and filter order (no. of taps) is complicated, as the article shows. It is not a simple linear relationship.
Regards,
Kral

 

[cafukarfoo]

Hello GertDalPozzo,

digital filter Passband width is influence by transition width.

Once you set the frequency cutoff, your passband width will be determined by the transition width.

If your transition width is smaller, that mean you have a wider passband width.

And in digital filter design, there is 3 factor influence each other:
1. transition width
2. filter order
3. passband/stopband ripple

You can only choose 2 parameter above for optimization, and you will sacrifice the parameter that being left behind.

Since you are interested to find the relationship between passband width and filter order,
we will set the passband/stopband ripple as constant.

So if you optimize transition width, your filter order going to be higher.

So that mean if you want wider passband, then your filter order going to be higher.

Hope this help.