# Wavelets? Dufuslets?

Started by February 15, 2017
```Given a complex-valued signal, extending from some negative frequency to
some positive frequency.

Is there some way to separate that signal into a bunch of overlapping
channels, regularly spaced, other than to have a bunch of filters all
running in parallel?

I'm thinking there has to be something clever involving FFTs, but I keep
utterly failing to figure it out.

To make it more concrete: say I sample the entire FM broadcast band, and
translate it down by 98MHz with a complex mixer.  Now I want to get
-10.1, -9.9, -9.7, etc., up to +10.1 -- all 201 channels (if I'm counting
right).

Assume that the sampling rate can be tailored to the problem, if it makes
a difference.

Clues appreciated.

Thank you.

--
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work!  See my website if you're interested
http://www.wescottdesign.com
```
```On Tue, 14 Feb 2017 23:48:25 -0600, Tim Wescott wrote:

> Given a complex-valued signal, extending from some negative frequency to
> some positive frequency.
>
> Is there some way to separate that signal into a bunch of overlapping
> channels, regularly spaced, other than to have a bunch of filters all
> running in parallel?
>
> I'm thinking there has to be something clever involving FFTs, but I keep
> utterly failing to figure it out.
>
> To make it more concrete: say I sample the entire FM broadcast band, and
> translate it down by 98MHz with a complex mixer.  Now I want to get
> -10.1, -9.9, -9.7, etc., up to +10.1 -- all 201 channels (if I'm
> counting right).
>
> Assume that the sampling rate can be tailored to the problem, if it
> makes a difference.
>
> Clues appreciated.
>
> Thank you.

Hmm.  If I'm doing my math right, given that I'm decimating (I forgot to
mention that...), 201 decimating band-pass filters are going to work
better.

If I'm really smart, I can use Rick Lyon's super-duper combination
lowpass-and-mix filter.  With decimation.  And hair on the floor because
I'll start by dotting all my 't's and crossing all my 'i's, then I won't
be able to tell which crossed 'i's are undotted 't's so I won't be able
to back out of my errors...

--
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work!  See my website if you're interested
http://www.wescottdesign.com
```
```On 15.02.2017 8:48, Tim Wescott wrote:
> Given a complex-valued signal, extending from some negative frequency to
> some positive frequency.
>
> Is there some way to separate that signal into a bunch of overlapping
> channels, regularly spaced, other than to have a bunch of filters all
> running in parallel?
>
> I'm thinking there has to be something clever involving FFTs, but I keep
> utterly failing to figure it out.
>
> To make it more concrete: say I sample the entire FM broadcast band, and
> translate it down by 98MHz with a complex mixer.  Now I want to get
> -10.1, -9.9, -9.7, etc., up to +10.1 -- all 201 channels (if I'm counting
> right).
>
> Assume that the sampling rate can be tailored to the problem, if it makes
> a difference.
>
> Clues appreciated.
>
> Thank you.
>

Tim, what you are looking for is explained in the book "Multirate Signal
Processing for Communication Systems" by fredric harris. The most
and 9 ("Polyphase channelizers").

With the caveat that it's one of the books you'd like to read entirely,
because it's just so well written! It's also the second most useful book
Digital Signal Processing" by Richard Lyons.

Hope that helps.

Gene

```
```On Wed, 15 Feb 2017 11:07:09 +0300, Evgeny Filatov wrote:

> On 15.02.2017 8:48, Tim Wescott wrote:
>> Given a complex-valued signal, extending from some negative frequency
>> to some positive frequency.
>>
>> Is there some way to separate that signal into a bunch of overlapping
>> channels, regularly spaced, other than to have a bunch of filters all
>> running in parallel?
>>
>> I'm thinking there has to be something clever involving FFTs, but I
>> keep utterly failing to figure it out.
>>
>> To make it more concrete: say I sample the entire FM broadcast band,
>> and translate it down by 98MHz with a complex mixer.  Now I want to get
>> -10.1, -9.9, -9.7, etc., up to +10.1 -- all 201 channels (if I'm
>> counting right).
>>
>> Assume that the sampling rate can be tailored to the problem, if it
>> makes a difference.
>>
>> Clues appreciated.
>>
>> Thank you.
>>
>>
> Tim, what you are looking for is explained in the book "Multirate Signal
> Processing for Communication Systems" by fredric harris. The most
> immediate answer would be to read chapters 6 ("Polyphase FIR filters")
> and 9 ("Polyphase channelizers").
>
> With the caveat that it's one of the books you'd like to read entirely,
> because it's just so well written! It's also the second most useful book
> Digital Signal Processing" by Richard Lyons.
>
> Hope that helps.
>
> Gene

Wow.  Thanks -- the term "polyphase filterbank" was all I needed.  And
it's extra-special good, because it turns out that I got my math extra-
special wrong, and pegged the polyphase technique as using way more
resources than it actually does (I think I multiplied by the decimation
factor, or something stupid like that).

At any rate -- once again I've invented a technology that already
exists.  It's nice to be able to cite it by name, though.

--

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

I'm looking for work -- see my website!
```
```[...snip...]
>
>At any rate -- once again I've invented a technology that already
>exists.  It's nice to be able to cite it by name, though.
>
>--
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com
>
>I'm looking for work -- see my website!

Invented or discovered?

Kudos to Gene for the fredric harris lower case respect.

Ced
---------------------------------------
Posted through http://www.DSPRelated.com
```
```On 15.02.2017 20:39, Tim Wescott wrote:

(snip)

>
> Wow.  Thanks -- the term "polyphase filterbank" was all I needed.  And
> it's extra-special good, because it turns out that I got my math extra-
> special wrong, and pegged the polyphase technique as using way more
> resources than it actually does (I think I multiplied by the decimation
> factor, or something stupid like that).
>
> At any rate -- once again I've invented a technology that already
> exists.  It's nice to be able to cite it by name, though.
>

You are welcome. Well, in the OP you've said most of the right words; I
just added a reference to the algorithm description.

For me, the use of a polyphase technique to implement a transmultiplexer
was the most emotional moment in the book. So I understand your
feelings. ;-)

Gene

```