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From: PaulTapper on 7 Jun 2010 08:18
Hi,

Is there a standard way of converting an IIR filter to a different sample
rate?

What I mean by this is, if I have an IIR filter F0 with a particular
frequency response at sample rate S0, and I want to create a filter F1 to
give, as near as possible, the same frequency response, at a different
sample rate S1, is there a standard way of calculating the coefficients of
F1 from F0?

My initial thoughts are that maybe I can find the zeroes and poles, and
then rotate them around the unit circle or something, but I suspect there
may be a standard solution to this problem?

Thanks for any help.

Paul


From: Jerry Avins on 7 Jun 2010 09:03
On 6/7/2010 8:18 AM, PaulTapper wrote:
> Hi,
>
> Is there a standard way of converting an IIR filter to a different sample
> rate?
>
> What I mean by this is, if I have an IIR filter F0 with a particular
> frequency response at sample rate S0, and I want to create a filter F1 to
> give, as near as possible, the same frequency response, at a different
> sample rate S1, is there a standard way of calculating the coefficients of
> F1 from F0?
>
> My initial thoughts are that maybe I can find the zeroes and poles, and
> then rotate them around the unit circle or something, but I suspect there
> may be a standard solution to this problem?

Why not design a new filter to the original response specs? Even if
there were a simple transformation, the prewarping would be wrong.

Jerry
--
Engineering is the art of making what you want from things you can get.
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From: Rune Allnor on 7 Jun 2010 09:52
On 7 Jun, 14:18, "PaulTapper" <paul__tapper(a)n_o_s_p_a_m.hotmail.com>
wrote:
> Hi,
>
> Is there a standard way of converting an IIR filter to a different sample
> rate?

No, there isn't. The normalized bandwidth is the main
design parameter for filters.

Suppose you want a LPF with passband 0-10 Hz. If the sampling
rate is low, say, 100 Hz, you will be able to achieve the goal
with a low-order filter.

If the sampling rate is high, say, 10kHz, you will need a far
higher filter order to meet the same spec.

Rune
From: Clay on 7 Jun 2010 11:20
On Jun 7, 8:18 am, "PaulTapper" <paul__tapper(a)n_o_s_p_a_m.hotmail.com>
wrote:
> Hi,
>
> Is there a standard way of converting an IIR filter to a different sample
> rate?
>
> What I mean by this is, if I have an IIR filter F0 with a particular
> frequency response at sample rate S0, and I want to create a filter F1 to
> give, as near as possible, the same frequency response, at a different
> sample rate S1, is there a standard way of calculating the coefficients of
> F1 from F0?
>
> My initial thoughts are that maybe I can find the zeroes and poles, and
> then rotate them around the unit circle or something, but I suspect there
> may be a standard solution to this problem?
>
> Thanks for any help.
>
> Paul

I'm with Jerry, on this one. Just redo the filter using your filter
design program. You may find that sometimes in order to meet spec, you
will have to increase the filter order.

Clay

From: robert bristow-johnson on 7 Jun 2010 11:44
On Jun 7, 11:20 am, Clay <c...(a)claysturner.com> wrote:
> On Jun 7, 8:18 am, "PaulTapper" <paul__tapper(a)n_o_s_p_a_m.hotmail.com>
> wrote:
>
>
>
> > Hi,
>
> > Is there a standard way of converting an IIR filter to a different sample
> > rate?
>
> > What I mean by this is, if I have an IIR filter F0 with a particular
> > frequency response at sample rate S0, and I want to create a filter F1 to
> > give, as near as possible, the same frequency response, at a different
> > sample rate S1, is there a standard way of calculating the coefficients of
> > F1 from F0?
>
> > My initial thoughts are that maybe I can find the zeroes and poles, and
> > then rotate them around the unit circle or something, but I suspect there
> > may be a standard solution to this problem?
>
> > Thanks for any help.
>
> I'm with Jerry, on this one. Just redo the filter using your filter
> design program. You may find that sometimes in order to meet spec, you
> will have to increase the filter order.

i'm with Clay and Rune and Jerry also. but if all of the "action" in
your filter (all of the resonant frequencies) are much much lower than
Nyquist, then the answer is "sorta yes". think of an analog filter as
a sorta digital filter with Nyquist bumped up to infinity. then all
of the resonant action *is* happening far below Nyquist and we know
how to simply scale s-plane coefficients in an analog filter to move
the frequency response around. so you can use a mapping like bilinear
transform to map your digital to analog, then scale the s-plane
coefficients in the simplistic manner, then map s-plane back to the z-
plane. but if you are reducing the sample rate, then you are pushing
the resonant action up toward Nyquist and then the approximations we
use that it's all far below Nyquist no longer apply.

r b-j



you can map an analo
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