# 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?

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.