Invariable FIR

Hello,

I am looking for a way to keep a FIR the same using to different
sampling rate.

I explain :
I havean an incoming signal sampling at 1048 Hz in which i want to
suppress everything above 50 Hz so i make a low-pass FIR filter (i
know a0, a1,.... filter coefficient). But i want to keep the same
filter behaviour with the same signal but sampling this time at 10008
Hz for example.

Is there a sample way to adjust my coefficient in order to obtain a
new filter of the same order which could suppress all above 50 Hz in
the same way as the initial one ?

"pardon_232000" <pardon_232000@yahoo.fr> wrote in message
news:ef9acc9e.0402141503.50c6bca8@posting.google.com...
> Hello,
>
> I am looking for a way to keep a FIR the same using to different
> sampling rate.
>
> I explain :
> I havean an incoming signal sampling at 1048 Hz in which i want to
> suppress everything above 50 Hz so i make a low-pass FIR filter (i
> know a0, a1,.... filter coefficient). But i want to keep the same
> filter behaviour with the same signal but sampling this time at 10008
> Hz for example.
>
> Is there a sample way to adjust my coefficient in order to obtain a
> new filter of the same order which could suppress all above 50 Hz in
> the same way as the initial one ?

Maybe, it depends on your requirements.

In essence what you want to do is to shrink the filter's frequency response
by a factor of 10008/1048.
So, in a really simple-minded way, this means you need to expand the
filter's time response by that same factor.
Expanding the time response means interpolating it so you'd need to pick an
expansion factor that makes sense like 9 or 10 instead of around 9.5.  It
means increasing the number of coefficients by a factor of 10.
A more detailed analysis would suggest that it's keeping the transition
width from passband to stopband that is driving this change - rather than
the passband width of the filter.

So, given those "facts", why not just design another filter that
approximates the parts of "sameness" that you need and see what you get?

Fred

In article <ef9acc9e.0402141503.50c6bca8@posting.google.com>,
pardon_232000 <pardon_232000@yahoo.fr> wrote:
>I am looking for a way to keep a FIR the same using to different
>sampling rate.
>
>I explain :
>I havean an incoming signal sampling at 1048 Hz in which i want to
>suppress everything above 50 Hz so i make a low-pass FIR filter (i
>know a0, a1,.... filter coefficient). But i want to keep the same
>filter behaviour with the same signal but sampling this time at 10008
>Hz for example.
>
>Is there a sample way to adjust my coefficient in order to obtain a
>new filter of the same order which could suppress all above 50 Hz in
>the same way as the initial one ?

If you have the equation for your low-pass FIR filter, then you just
need to expand it in the time domain by fnew/fold and recalculate all
the coefficients (the number of which will expand by about the same
amount).

If you don't have or can't construct the equation for your FIR
coefficients, then you could still expand the filter coefficients in
the time domain (e.g. plot points at 0, 9.55, 19.1,...) and polynomial
interpolate (Lagrange, spline, Bezier, sinc, etc.) at all the integer
abscissi (at 0, 1, 2,...) for your new coefficients.  However, this will
introduce distortions if you don't start with enough original taps, or
the filter is too wide in the frequency domain for your interpolation
method.

Another possibility would be to downsample your original signal by
1048/10008 (~ 1/9.55) while filtering to the Nyquist f, and then run
your FIR filter on that intermediate filtered signal.


IMHO. YMMV.
-- 
Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/ 
#include <canonical.disclaimer>        // only my own opinions, etc.