Filter values in multi-stage audio sample rate covnersion?

Hello,

if I make a sample rate conversion using multi-stages (e.g. 48 kHz
downto to 44.1 kHz in 3 stages with the ratios 3/6, 7/4 and 7/5), do I
need different filter coefficients for the 3 filters or can I use
always the same filter, when the audio data frequence range itself is
limited to something like 22 kHz???



Thanks for your help!

damc

damc4 wrote:
> Hello,
> 
> if I make a sample rate conversion using multi-stages (e.g. 48 kHz
> downto to 44.1 kHz in 3 stages with the ratios 3/6, 7/4 and 7/5), do I
> need different filter coefficients for the 3 filters or can I use
> always the same filter, when the audio data frequence range itself is
> limited to something like 22 kHz???

Although the absolute cutoff frequency can be the same, the normalized 
frequency (that is, fc/Fs) will be different for each stage. 
Unfortunately for you, digital filters only pay attention to the 
normalized frequency.

BTW, your stages don't multiply out to 44.1/48.  3/6 should be 3/8 (typo?).

Also, if you make the first stage 3/8, you're going to lose some serious 
bandwidth, as the sample rate between the first and second stages will 
be a mere 18 KHz.

This has the additional implication that the first stage (if it's 3/8) 
cannot have a cutoff of ~22.05 KHz (it'll HAVE to be less than 9 KHz).

-- 
Jim Thomas            Principal Applications Engineer  Bittware, Inc
jthomas@bittware.com  http://www.bittware.com    (603) 226-0404 x536
In theory, theory and practice are the same, but in practice, they're not

"Jim Thomas" <jthomas@bittware.com> wrote in message 
news:11bo2sgjouka4a5@corp.supernews.com...
> damc4 wrote:
>> Hello,
>>
>> if I make a sample rate conversion using multi-stages (e.g. 48 kHz
>> downto to 44.1 kHz in 3 stages with the ratios 3/6, 7/4 and 7/5), do I
>> need different filter coefficients for the 3 filters or can I use
>> always the same filter, when the audio data frequence range itself is
>> limited to something like 22 kHz???
>
> Although the absolute cutoff frequency can be the same, the normalized 
> frequency (that is, fc/Fs) will be different for each stage. Unfortunately 
> for you, digital filters only pay attention to the normalized frequency.
>
> BTW, your stages don't multiply out to 44.1/48.  3/6 should be 3/8 
> (typo?).
>
> Also, if you make the first stage 3/8, you're going to lose some serious 
> bandwidth, as the sample rate between the first and second stages will be 
> a mere 18 KHz.
>
> This has the additional implication that the first stage (if it's 3/8) 
> cannot have a cutoff of ~22.05 KHz (it'll HAVE to be less than 9 KHz).
>
> -- 
> Jim Thomas            Principal Applications Engineer  Bittware, Inc
> jthomas@bittware.com  http://www.bittware.com    (603) 226-0404 x536
> In theory, theory and practice are the same, but in practice, they're not


fwiw...a month ago I posted some Simulink (R14SP2) models that illustrate 
almost this exact application here:

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=7743&objectType=file

There are floating-point and fixed-point example versions available there.

And yes, Jim is correct - the coefficients are different for every 
stage...and it is very important that the first filter stage does not lower 
the sampling frequency (in order to not lose your high fidelity audio 
spectrum right from the start...)

Steve

Hello,

Jim, yes it was just a typo, 147/160 is the ratio, so it must be 3/8.
Jim and Steve, and again yes, I didn't cared for the posting about the
stage order.
I am aware that I shouldn't go below my destination frequency during
the conversion.
Steve, thanks for the link, I will have a look on it.

And thanks for the help. that was the hint I was looking for.

Damc

"damc4" <damc4@gmx.de> wrote in message
news:1119618058.260243.312230@g49g2000cwa.googlegroups.com...
> Hello,
>
> if I make a sample rate conversion using multi-stages (e.g. 48 kHz
> downto to 44.1 kHz in 3 stages with the ratios 3/6, 7/4 and 7/5), do I
> need different filter coefficients for the 3 filters or can I use
> always the same filter, when the audio data frequence range itself is
> limited to something like 22 kHz???

Just curious, what is the advantage of doing the 48/44.1 conversion in 3 stages
versus a single stage?

Jon Harris wrote:
> Just curious, what is the advantage of doing the 48/44.1 conversion in 3 stages
> versus a single stage?
> 

It can be cheaper.  To realize some computational savings, you can use 
sloppy filters in the initial stages, so long as you protect the 
intergity of the /final/ passband.  You can trash major portions of the 
intermediate passbands (by allowing aliasing), so long as you keep the 
trash out of the final passband.

It always takes me a lot of work with pencil and paper to get my head 
around this in the interp/decimiate situation, but it's fairly 
straightforward in a decimate-only or interpolate-only scenario.

Rick covers this in his book (pg 384 and onward of the 2nd edition).

-- 
Jim Thomas            Principal Applications Engineer  Bittware, Inc
jthomas@bittware.com  http://www.bittware.com    (603) 226-0404 x536
Failure is always an option

In article <11c0kjpo1s7ioeb@corp.supernews.com>,
Jon Harris <jon_harrisTIGER@hotmail.com> wrote:
>Just curious, what is the advantage of doing the 48/44.1 conversion in
>3 stages versus a single stage?

I wonder if the OP was planning on using IIR/recursive filters instead
of linear phase FIR filters for resampling.


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

Ronald H. Nicholson Jr. schrieb:
> In article <11c0kjpo1s7ioeb@corp.supernews.com>,
> Jon Harris <jon_harrisTIGER@hotmail.com> wrote:
> >Just curious, what is the advantage of doing the 48/44.1 conversion in
> >3 stages versus a single stage?
>
> I wonder if the OP was planning on using IIR/recursive filters instead
> of linear phase FIR filters for resampling.
>
>
> IMHO. YMMV.
> --
> Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/
> #include <canonical.disclaimer>        // only my own opinions, etc.

Hi Ron,

no.
my target is an FPGA and I have no problems concerning performance or
resource utilisation, so I realize it in the simplest way with FIRs.

damc

Jim Thomas wrote:
> Jon Harris wrote:
> 
>> Just curious, what is the advantage of doing the 48/44.1 conversion in 
>> 3 stages
>> versus a single stage?
>>
> 
> It can be cheaper.  To realize some computational savings, you can use 
> sloppy filters in the initial stages, so long as you protect the 
> intergity of the /final/ passband.  You can trash major portions of the 
> intermediate passbands (by allowing aliasing), so long as you keep the 
> trash out of the final passband.
> 
> It always takes me a lot of work with pencil and paper to get my head 
> around this in the interp/decimiate situation, but it's fairly 
> straightforward in a decimate-only or interpolate-only scenario.
> 
> Rick covers this in his book (pg 384 and onward of the 2nd edition).
> 

It often makes the filter design easier as well. For instance to do a 
single stage decimation by 1024, would likely require a huge number of 
taps. This single filter may be impossible to design using the PM 
algorithm - Even in matlab, the  filter length can usually only go to 
~1200 taps before instabilities start to occur (YMMV).

By breaking it up into several stages (because of the sloppier filters) 
the filter lengths are reduced, and thus you're able to design them.

These ideas are clearly discussed in Crochiere & Rabiner's "Multirate 
Signal Processing"

Cheers,
David

"David Kirkland" <spam@netscape.net> wrote in message
news:XQawe.1493$Ai.282292@news20.bellglobal.com...
> Jim Thomas wrote:
> > Jon Harris wrote:
> >
> >> Just curious, what is the advantage of doing the 48/44.1 conversion in
> >> 3 stages
> >> versus a single stage?
> >>
> >
> > It can be cheaper.  To realize some computational savings, you can use
> > sloppy filters in the initial stages, so long as you protect the
> > intergity of the /final/ passband.  You can trash major portions of the
> > intermediate passbands (by allowing aliasing), so long as you keep the
> > trash out of the final passband.
> >
> > It always takes me a lot of work with pencil and paper to get my head
> > around this in the interp/decimiate situation, but it's fairly
> > straightforward in a decimate-only or interpolate-only scenario.
> >
> > Rick covers this in his book (pg 384 and onward of the 2nd edition).
> >
>
> It often makes the filter design easier as well. For instance to do a
> single stage decimation by 1024, would likely require a huge number of
> taps. This single filter may be impossible to design using the PM
> algorithm - Even in matlab, the  filter length can usually only go to
> ~1200 taps before instabilities start to occur (YMMV).

I agree with you when the resampling involves decimation only (or interp
only). In this case, the resampling is from 48 to 44.1 which shouldn't need
a very large filter. So in this specific case, I wouldn't say the filter
design is consierably easier. Yes - the multi-stage approach could use
sloppier filters but a straight conversion wouldn't result in a > 1000 taps
filter (I've never done this but that's what my gut feel tells me...unless
the required stop band attenuation is way way down there).

Cheers
Bhaskar

> By breaking it up into several stages (because of the sloppier filters)
> the filter lengths are reduced, and thus you're able to design them.
>
> These ideas are clearly discussed in Crochiere & Rabiner's "Multirate
> Signal Processing"
>
> Cheers,
> David