Overlapping sub bands in WOLA channelizer

Hi,
I would like to create a WOLA channelizer with overlapping passbands,
say 25%, but I'm struggling to see how I could do this as my math
isn't up to it.
I can imagine having two channelizers operating on overlapping input
samples and then interleaving the output from the channelizers to
increase the sample rate but I'm pretty sure this doesn't get me much
closer.
Anyone been down this road before?

On Apr 8, 3:53=A0pm, Paul Green <dc.to...@gmail.com> wrote:
> Hi,
> I would like to create a WOLA channelizer with overlapping passbands,
> say 25%, but I'm struggling to see how I could do this as my math
> isn't up to it.
> I can imagine having two channelizers operating on overlapping input
> samples and then interleaving the output from the channelizers to
> increase the sample rate but I'm pretty sure this doesn't get me much
> closer.
> Anyone been down this road before?

What you need is fairly straightforward. It all comes down to the
design of the window that you use. If your window has length N and
your FFT has length M, then the time-aliasing factor is K =3D N/M (i.e.
you sum K blocks of M samples together before doing your FFT). The
window effectively operates at the higher sample rate, since it is
applied before the time aliasing is done. For a low-overlap
filterbank, like you might use for a spectrum analyzer application,
you would design a window whose one-sided bandwidth is approximately
equal to pi/(2*M). Using whatever filter-design technique you like,
you can get just about any response that you want, as the window is
typically pretty long (K times your FFT size), giving you tight
control over passband flatness and filter overlap.

For your application, this is no different. You just need to design
the window to have the spectral shape that meets your requirements.
The channels in the WOLA filterbank are evenly spaced by 2*pi/M in
normalized frequency, so you just design the window such that its
transition region overlaps its neighboring filters in the way that you
want.

That doesn't seem like a very clear explanation but it's the best I
can think of at the moment. Does this make sense to you?

Jason

On Apr 8, 12:53=A0pm, Paul Green <dc.to...@gmail.com> wrote:
> Hi,
> I would like to create a WOLA channelizer with overlapping passbands,
> say 25%, but I'm struggling to see how I could do this as my math
> isn't up to it.
> I can imagine having two channelizers operating on overlapping input
> samples and then interleaving the output from the channelizers to
> increase the sample rate but I'm pretty sure this doesn't get me much
> closer.
> Anyone been down this road before?

Take a look at the discussion late in this paper, figure 25 in
particular:

WINDOWS: Finite Aperture Effects and Applications in Signal Processing
fred harris,
San Diego State University
http://www.signumconcepts.com/download/paper033.pdf

Note, this is not THE classic harris windows paper, but another.

Dale B. Dalrymple

On 04/08/2011 12:53 PM, Paul Green wrote:
> Hi,
> I would like to create a WOLA channelizer with overlapping passbands,
> say 25%, but I'm struggling to see how I could do this as my math
> isn't up to it.
> I can imagine having two channelizers operating on overlapping input
> samples and then interleaving the output from the channelizers to
> increase the sample rate but I'm pretty sure this doesn't get me much
> closer.
> Anyone been down this road before?

What the heck does WOLA stand for?

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

On Apr 8, 6:42=A0pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On 04/08/2011 12:53 PM, Paul Green wrote:
>
> > Hi,
> > I would like to create a WOLA channelizer with overlapping passbands,
> > say 25%, but I'm struggling to see how I could do this as my math
> > isn't up to it.
> > I can imagine having two channelizers operating on overlapping input
> > samples and then interleaving the output from the channelizers to
> > increase the sample rate but I'm pretty sure this doesn't get me much
> > closer.
> > Anyone been down this road before?
>
> What the heck does WOLA stand for?
>
> --
>
> Tim Wescott
> Wescott Design Serviceshttp://www.wescottdesign.com
>
> Do you need to implement control loops in software?
> "Applied Control Theory for Embedded Systems" was written for you.
> See details athttp://www.wescottdesign.com/actfes/actfes.html

Weighted Over Lap Add

On Friday, April 8, 2011 at 4:06:23 PM UTC-6, dbd wrote:
> On Apr 8, 12:53=C2=A0pm, Paul Green <dc.to...@gmail.com> wrote:
> > Hi,
> > I would like to create a WOLA channelizer with overlapping passbands,
> > say 25%, but I'm struggling to see how I could do this as my math
> > isn't up to it.
> > I can imagine having two channelizers operating on overlapping input
> > samples and then interleaving the output from the channelizers to
> > increase the sample rate but I'm pretty sure this doesn't get me much
> > closer.
> > Anyone been down this road before?
>=20
> Take a look at the discussion late in this paper, figure 25 in
> particular:
>=20
> WINDOWS: Finite Aperture Effects and Applications in Signal Processing
> fred harris,
> San Diego State University
> http://www.signumconcepts.com/download/paper033.pdf
>=20
> Note, this is not THE classic harris windows paper, but another.
>=20
> Dale B. Dalrymple

Does this paper still exist? The link seems to be broken: http://www.signum=
concepts.com/download/paper033.pdf

On Friday, April 21, 2017 at 10:54:37 AM UTC-7, seth....@gmail.com wrote:
> On Friday, April 8, 2011 at 4:06:23 PM UTC-6, dbd wrote:
> > 
> > Take a look at the discussion late in this paper, figure 25 in
> > particular:
> > 
> > WINDOWS: Finite Aperture Effects and Applications in Signal Processing
> > fred harris,
> > San Diego State University
> > http://www.signumconcepts.com/download/paper033.pdf
> > 
> > Note, this is not THE classic harris windows paper, but another.
> > 
> > Dale B. Dalrymple
> 
> Does this paper still exist? The link seems to be broken: http://www.signumconcepts.com/download/paper033.pdf

I assume all the big kids have Googled on the title and author to look for a current location for the paper. 

For the little kids, take a look today at:

http://bnordgren.org/seismo/UNP-Harris.pdf

(Google is your friend.)

If anyone wants to find the paper tomorrow or in another 6 years, take a shot at being a big kid.

Dale B. Dalrymple

On Friday, April 8, 2011 at 9:01:50 PM UTC-4, John wrote:
> On Apr 8, 6:42&nbsp;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> >
> > What the heck does WOLA stand for?
> >
> 
> Weighted Over Lap Add

i always thought that the "W" was for "Windowed", but i googled it and you're right.  i think that if i find some old paper from the 70s it might say the W is for Windowed, but maybe not.

then i had always thought that "WSOLA" was "Windowed Synchronous Overlap Add" and i find out it's "Waveform Similarity and Overlap Add".

funny thing is, that the two terms end up meaning about the same thing in the algorithms.  for either WOLA or WSOLA.

i think that PSOLA means "Pitch Synchronous Overlay Add" and, even though originally i couldn't see that it was much different than WSOLA, since then the term has come to mean what i usually call "Lent's Algorithm", which could also be attributed to a French guy named "Hamon".

r b-j

robert bristow-johnson wrote:
> On Friday, April 8, 2011 at 9:01:50 PM UTC-4, John wrote:
>> On Apr 8, 6:42 pm, Tim Wescott <t...@seemywebsite.com> wrote:
>>>
>>> What the heck does WOLA stand for?
>>>
>>
>> Weighted Over Lap Add
>
> i always thought that the "W" was for "Windowed", but i googled it
> and you're right.  i think that if i find some old paper from the 70s
> it might say the W is for Windowed, but maybe not.
>

Sometimes windowing and weighting are used interchangeably.

> then i had always thought that "WSOLA" was "Windowed Synchronous
> Overlap Add" and i find out it's "Waveform Similarity and Overlap
> Add".
>
RAS is redundant acronym syndrome syndrome.

https://en.wikipedia.org/wiki/RAS_syndrome

> funny thing is, that the two terms end up meaning about the same
> thing in the algorithms.  for either WOLA or WSOLA.
>
> i think that PSOLA means "Pitch Synchronous Overlay Add" and, even
> though originally i couldn't see that it was much different than
> WSOLA, since then the term has come to mean what i usually call
> "Lent's Algorithm", which could also be attributed to a French guy
> named "Hamon".
>
> r b-j
>

-- 
Les Cargill