# multirate filtering and computational gain

Started by September 21, 2006
```It is stated that in case of narrow transition band filters, multirate
filtering provides us with a computational efficiency as compare to
standard time invariant filters. The idea is to reduce the sampling rate
(less number of samples) and to use simple, low order filters (less number
of operations per input sample), instead of using a single high order
filter operates at fixed high sampling rate.

But whats about the cost of filter calculation (design). It does not seem
that in case of multi stage filtering where we have to calculate several
filters the over all computational gain is reduced as compare to the
standard case.

Thnaks in advance for the ideas and discussion.

```
```renaudin skrev:
> It is stated that in case of narrow transition band filters, multirate
> filtering provides us with a computational efficiency as compare to
> standard time invariant filters. The idea is to reduce the sampling rate
> (less number of samples) and to use simple, low order filters (less number
> of operations per input sample), instead of using a single high order
> filter operates at fixed high sampling rate.
>
> But whats about the cost of filter calculation (design). It does not seem
> that in case of multi stage filtering where we have to calculate several
> filters the over all computational gain is reduced as compare to the
> standard case.

A very interesting observation: In order to gain run-time speed-ups,
the designer needs to spend a lot more time on making the filters,
than is needed in the "standard" case. Or spend \$\$ on a faster
processor.

I agree with your observation, but I don't necessarily see it as a
problem.

In filter design, as in most aspects of life, there is no such thing as

a free lunch. If you want anything more than a bare minimum,
you'll have to pay for it in one sense or another. If you want the
reduced run time of multirate filters, you'll have to pay in the sense
that you will have to use more elaborate techniques (SW programs)
or time to actually design the filters. It is just the same way lots of

pay \$\$ to get  a fast DSP, or spend a lot of time and skills
optimizing assembly code.

Rune

```
```Rune Allnor wrote:
> renaudin skrev:
>> It is stated that in case of narrow transition band filters, multirate
>> filtering provides us with a computational efficiency as compare to
>> standard time invariant filters. The idea is to reduce the sampling rate
>> (less number of samples) and to use simple, low order filters (less number
>> of operations per input sample), instead of using a single high order
>> filter operates at fixed high sampling rate.
>>
>> But whats about the cost of filter calculation (design). It does not seem
>> that in case of multi stage filtering where we have to calculate several
>> filters the over all computational gain is reduced as compare to the
>> standard case.
>
> A very interesting observation: In order to gain run-time speed-ups,
> the designer needs to spend a lot more time on making the filters,
> than is needed in the "standard" case. Or spend \$\$ on a faster
> processor.
>
> I agree with your observation, but I don't necessarily see it as a
> problem.
>
> In filter design, as in most aspects of life, there is no such thing as
>
> a free lunch. If you want anything more than a bare minimum,
> you'll have to pay for it in one sense or another. If you want the
> reduced run time of multirate filters, you'll have to pay in the sense
> that you will have to use more elaborate techniques (SW programs)
> or time to actually design the filters. It is just the same way lots of
>
> pay \$\$ to get  a fast DSP, or spend a lot of time and skills
> optimizing assembly code.
>
> Rune
>

Rune, I agree with you in spirit.  However, multirate DSP is not all
that hard, plus the alternative is often not as simple as simply getting
a faster processor.

Multistage techniques make things easy that would be completely
impractical with the simple approach.

For example: Say you want to filter some feature of a signal with a FIR
filter having a transition band that is a millionth of the input
sampling rate.

Without multirate, you'd need a FIR with many millions of taps.

With multirate, you can use 3 stages with a few hundred taps each.

--
Mark Borgerding

```
```renaudin wrote:
> It is stated that in case of narrow transition band filters, multirate
> filtering provides us with a computational efficiency as compare to
> standard time invariant filters. The idea is to reduce the sampling rate
> (less number of samples) and to use simple, low order filters (less number
> of operations per input sample), instead of using a single high order
> filter operates at fixed high sampling rate.
>
> But whats about the cost of filter calculation (design). It does not seem
> that in case of multi stage filtering where we have to calculate several
> filters the over all computational gain is reduced as compare to the
> standard case.
>
> Thnaks in advance for the ideas and discussion.

Anybody can build a wooden bridge. Most people with some experience and
a few rules of thumb can build a wooden bridge that will stand. A civil
engineer can build a wooden bridge that will stand, using less than half
the amount of timber. When timber is cheap, his skill isn't worth much.

A product is designed once but built many times. When I worked for RCA,
an engineer who managed to make a TV chassis a nickel cheaper without
compromising quality got much praise and a modest bonus.

Pride of workmanship is involved as well.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```There are still other considerations:

For offline processing you have to consider the cost of sitting around
waiting for results.

Using multi-rate processing I once cut processing of 30 minutes of
audio from something like 60 minutes to 90 seconds.  The software was
run alot.  Saved the customer lots of time and money.

Dirk Bell
DSP Consultant

renaudin wrote:
> It is stated that in case of narrow transition band filters, multirate
> filtering provides us with a computational efficiency as compare to
> standard time invariant filters. The idea is to reduce the sampling rate
> (less number of samples) and to use simple, low order filters (less number
> of operations per input sample), instead of using a single high order
> filter operates at fixed high sampling rate.
>
> But whats about the cost of filter calculation (design). It does not seem
> that in case of multi stage filtering where we have to calculate several
> filters the over all computational gain is reduced as compare to the
> standard case.
>
> Thnaks in advance for the ideas and discussion.

```