# Filter Bank theory

Started by June 22, 2009
```Hello,

I am reading a paper about filter bank theory and I need help in
understanding something.

Say a filter bank (FB) contains M analysis and M synthesis filters.
Since the effective bandwidth of each subband signal is pi/M, it can
be downsampled to reduce the total rate.

How can downsampling not introduce aliasing? For example if Fs = 360
and one of the bands is 240-270Hz, then wouldn't downsampling this
band by any factor introduced aliasing?

Thanks,
--ayyaz.
```
```On Mon, 22 Jun 2009 15:05:02 -0700, ayyaz ayyaz wrote:

> Hello,
>
> I am reading a paper about filter bank theory and I need help in
> understanding something.
>
> Say a filter bank (FB) contains M analysis and M synthesis filters.
> Since the effective bandwidth of each subband signal is pi/M, it can be
> downsampled to reduce the total rate.
>
> How can downsampling not introduce aliasing? For example if Fs = 360 and
> one of the bands is 240-270Hz, then wouldn't downsampling this band by
> any factor introduced aliasing?
>
> Thanks,
> --ayyaz.

Nyquist didn't say that:  http://www.wescottdesign.com/articles/Sampling/
sampling.html.

--
www.wescottdesign.com
```
```On Jun 22, 6:05&#2013266080;pm, ayyaz ayyaz <ayya...@gmail.com> wrote:
> Hello,
>
> I am reading a paper about filter bank theory and I need help in
> understanding something.
>
> Say a filter bank (FB) contains M analysis and M synthesis filters.
> Since the effective bandwidth of each subband signal is pi/M, it can
> be downsampled to reduce the total rate.
>
> How can downsampling not introduce aliasing? For example if Fs = 360
> and one of the bands is 240-270Hz, then wouldn't downsampling this
> band by any factor introduced aliasing?
>
> Thanks,
> --ayyaz.

Sort of. I imagine people will disagree on the proper terminology to
use for this bandpass sampling, but I like to think of it as
"intended" aliasing. Yes, if you sample at 360 Hz, the band from 240
to 270 Hz will appear to be at a lower frequency, which is aliasing.
But, since your analysis filter blocked out all other frequencies,
there aren't any other components that land on top of the band of
interest. So, while it might technically be aliasing, you don't get
any interference with your desired passband.

Jason
```
```On Jun 22, 3:05 pm, ayyaz ayyaz <ayya...@gmail.com> wrote:
> Hello,
>
.> I am reading a paper about filter bank theory and I need help in
.> understanding something.

Don't you think you would get more useful answers if you told us about
the particular filter bank theory in the paper or the source/title of
the paper or both?

>
> Say a filter bank (FB) contains M analysis and M synthesis filters.
> Since the effective bandwidth of each subband signal is pi/M, it can
> be downsampled to reduce the total rate.
>
.> How can downsampling not introduce aliasing?

If it is accompanied (or preceded) by antialias filtering. The nature
of the anti-alias filtering depends on the form of the filter bank
(which you haven't told us) and the desampling among other things.

>For example if Fs = 360
.> and one of the bands is 240-270Hz, then wouldn't downsampling this
.> band by any factor introduced aliasing?

It could but it need not, depending on what you mean by filter bank,
and how you choose your filtering and your desampling. If you want a