# Applying FIR filter to data with different sample rates

I have a filter design, and it filters over a 1-2 kHz range.
What should I do if I want to apply it to data with a different sample rate than the one for which it was designed?

Let's say it consists of Bessel and Chebyshev filters. How do I find a function that defines each filter's coefficients at an arbitrary sample rate? Or should I do this by hand?

## 1 Answer

Since you mention sampling, you are presumably talking of a digital filter.

The cut-off frequency or half-power frequency of a digital filter is actually relative to the sampling frequency $f_s$. If your digital filter is passing signals in the $1$ kHz to $2$ kHz range when you feed it a signal sampled at $f_s = 20$ kHz, then the pass band is from $5\%$ to $10\%$ of $f_s$. These ratios do not change if $f_s$ changes to some other value, say $40$ kHz. The same digital filter will become a filter with passband $2$ kHz to $4$ kHz without your having to do anything.

• But I want passband at 1-2 KHz at arbitrary sample rate. I made quick calculations and it seems like coefficients from some filter parts are correlated, but not all. So do I need to reshape filters for fixed sample rates, or there is hope in quest for function/approach that calculates this coefficient for arbitrary sample rate? – zetah Jan 9 '12 at 16:07
• If you want a filter to have fixed pass band at different sampling rates, you need to modify the coefficients accordingly. The results can be messy: see, for example, this answer which describes the calculations needed for a very simple filter. – Dilip Sarwate Jan 9 '12 at 16:19
• OK, thanks. I'll range filter at fixed rates by hand. I took a look at pointed answer... maybe I'll open my workbook and do some math, but I doubt my skills ;) – zetah Jan 9 '12 at 16:29