Filter values in multi-stage audio sample rate covnersion?

"Bhaskar Thiagarajan" <bhaskart@deja.com> wrote in message 
news:42c17fe1$0$18640$14726298@news.sunsite.dk...
> "David Kirkland" <spam@netscape.net> wrote in message
> news:XQawe.1493$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
>> > integrity 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/decimate 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).

There are some tricks you can use to make the filter design easier for these 
huge filters.  The windowed sinc method with a hand-tweaked kaiser window can 
usually get pretty close to a PM filter and doesn't suffer from any numerical 
issues at large sizes.  Or you can  design the filter at 1/2 (or 1/4, etc.) the 
size you need (e.g. design to decimate by 512 instead of 1024) and then 
interpolate up to get the full-length filter.  The filter coefficients are 
usually so heavily oversampled (smooth) that linear interpolation is good 
enough.

> 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).

Because of the strange sample rate ratio (147/160), you probably will need a > 
1000 tap filter for any kind of decent stop-band for audio.  The way I think of 
it in my mind is that the ratio essentially forces you to oversample your filter 
by 160x (or maybe 147x?), so it doesn't take a very long "normal" filter before 
the "oversampled" filter is > 1000 taps.