Filter design with 'freqsamp' method?

"robert bristow-johnson" <rbj@audioimagination.com> wrote in message 
news:c2f65e9b-74e2-41e3-85f0-61684db85f48@k39g2000yqd.googlegroups.com...

> well, i'm still trying to pin these guys down.  if their r.m.s. delay
> parameter ("spread" or whatever it's called) is a measure of deviation
> from phase linearity, then nothing can beat a phase linear FIR.

I don't know if there's a formal definition.
I just assumed it was a measure of the dispersiveness
(frequency dependent delay) of the filter.

> but if it's a measure of phase delay or group delay (from zero),
> then minimum-phase filter will beat linear-phase.

True, but I'm not sure why anybody would refer to that
as "spread".

Pete 

Steve Pope <spope33@speedymail.org> wrote:

>robert bristow-johnson  <rbj@audioimagination.com> wrote:

>>well, i'm still trying to pin these guys down.  if their r.m.s. delay
>>parameter ("spread" or whatever it's called) is a measure of deviation
>>from phase linearity, then nothing can beat a phase linear FIR.  but
>>if it's a measure of phase delay or group delay (from zero), then a
>>minimum-phase filter will beat linear-phase.

>It is neither.

Here's a reference:

Ibnkahla, _Signal Processing for Mobile Communications Handbook_,
section 1.2.2.1.4.  It is viewable on Google Books.

He used the same expression for average delay I stated, but
his expression for RMS Delay Spread is a little different,
and I don't like it as much, but I think his expression is
as close to a standard definition as you will get.

RMS delay spread must be used carefully; there are responses with
large RMS delay spreads which do not have bad phase qualities for
a most signals, i.e.  something like

      h(t) = 1*(t) + 100*(t - 20) - 100*(t - 20.0001)



S.

robert bristow-johnson wrote:
> On Jul 1, 10:59 am, Fred Marshall <fmarshallx@remove_the_xacm.org>
> wrote:
>> r b-j,
>>
>> Well, maybe I've had it wrong all these years but I'd say that the
>> windowing method starts with N frequency samples where N is the length
>> of the filter you want.
> 
> so then, since the DFT and iDFT are bijective (i love using fancy-
> pants words), why window?  if h[n] has N samples and N degrees of
> freedom, so does H[k].  you specify your N frequency samples and you
> can hit it perfectly with no windowing.
> 
> so, that seems curious to me.
> 
> r b-j

You window because the frequency response between those points can be 
nasty.  Either you don't window and convolve those samples with a 
matching sinc er.. Dirichlet or you window and convolve those samples 
with something else.

The trade is that the Dirichlet matches all the samples exactly.  Other 
windows don't.  Some match them all except the adjacent two as in the 
1/2  1  1/2 sum of adjacent Dirichlets.  It still has zeros in the sum 
at all the other sample points - so the convolution doesn't perturb 
their values.  And, the values between points are better behaved.

And making N larger to begin with doesn't affect any of this in my way 
of looking at it.

Fred

Pete Fraser <pfraser@covad.net> wrote:

>"robert bristow-johnson" <rbj@audioimagination.com> wrote in message 

>> well, i'm still trying to pin these guys down.  if their r.m.s. delay
>> parameter ("spread" or whatever it's called) is a measure of deviation
>> from phase linearity, then nothing can beat a phase linear FIR.

>I don't know if there's a formal definition.
>I just assumed it was a measure of the dispersiveness
>(frequency dependent delay) of the filter.

So as to save you guys some googling I have uploaded Ibnkahla's
definition of RMS delay spread to the following link which
I will leave in place for a few days.

Hopefully this makes things less ambiguous.

http://www.rahul.net/spp/IbnkahlaDelaySpread.bmp

Steve

On Sun, 4 Jul 2010 16:15:35 +0000 (UTC), spope33@speedymail.org (Steve Pope)
wrote:

>So as to save you guys some googling I have uploaded Ibnkahla's
>definition of RMS delay spread to the following link which
>I will leave in place for a few days.
>
>Hopefully this makes things less ambiguous.
>
>http://www.rahul.net/spp/IbnkahlaDelaySpread.bmp

I only gave it a cursory look, but comparing that with the discussion of moments
that I put into US Patent 5375067, Ibnkahla's definition of RMS delay spread
appears to be the same as RMS Duration.

Greg

On Jul 4, 1:35&#4294967295;pm, Greg Berchin <gberc...@comicast.net.invalid> wrote:
> On Sun, 4 Jul 2010 16:15:35 +0000 (UTC), spop...@speedymail.org (Steve Pope)
> wrote:
>
> >So as to save you guys some googling I have uploaded Ibnkahla's
> >definition of RMS delay spread to the following link which
> >I will leave in place for a few days.
>
> >Hopefully this makes things less ambiguous.

might be if i knew what P(t) is.

> >http://www.rahul.net/spp/IbnkahlaDelaySpread.bmp
>
> I only gave it a cursory look, but comparing that with the discussion of moments
> that I put into US Patent 5375067, Ibnkahla's definition of RMS delay spread
> appears to be the same as RMS Duration.

can you define that in terms of impulse response, h(t)?

otherwise i'm still confused.

r b-j

robert bristow-johnson  <rbj@audioimagination.com> wrote:

>> On Sun, 4 Jul 2010 16:15:35 +0000 (UTC), spop...@speedymail.org (Steve Pope)

>> >So as to save you guys some googling I have uploaded Ibnkahla's
>> >definition of RMS delay spread to the following link which
>> >I will leave in place for a few days.

>> >Hopefully this makes things less ambiguous.

>might be if i knew what P(t) is.

For the full details, enough of Ibnakahla's text (see my previous
post) is on Google books to extract those.

I think he wants P(tau) to be the power delay profile, but another
possibility is the just magnitude of the impulse response.

(So, yes, still ambiguous.)

S.

On Sun, 4 Jul 2010 17:30:48 -0700 (PDT), robert bristow-johnson
<rbj@audioimagination.com> wrote:

>can you define that in terms of impulse response, h(t)?

In the case of the RMS Duration, it is simply the normalized second moment of a
generic time domain waveform, so h(t) will do nicely.

In the case of Ibnkahla's RMS delay spread, I interpreted P(tau) to be something
like h(t-tau), where tau is the temporal centroid.  If P(t) is something else,
then I don't know.

Greg

Fred Marshall wrote:
> robert bristow-johnson wrote:
>> On Jul 1, 10:59 am, Fred Marshall <fmarshallx@remove_the_xacm.org>
>> wrote:
>>> r b-j,
>>>
>>> Well, maybe I've had it wrong all these years but I'd say that the
>>> windowing method starts with N frequency samples where N is the length
>>> of the filter you want.
>>
>> so then, since the DFT and iDFT are bijective (i love using fancy-
>> pants words), why window?  if h[n] has N samples and N degrees of
>> freedom, so does H[k].  you specify your N frequency samples and you
>> can hit it perfectly with no windowing.
>>
>> so, that seems curious to me.
>>
>> r b-j
> 
> You window because the frequency response between those points can be 
> nasty.  Either you don't window and convolve those samples with a 
> matching sinc er.. Dirichlet or you window and convolve those samples 
> with something else.
> 
> The trade is that the Dirichlet matches all the samples exactly.  Other 
> windows don't.  Some match them all except the adjacent two as in the 
> 1/2  1  1/2 sum of adjacent Dirichlets.  It still has zeros in the sum 
> at all the other sample points - so the convolution doesn't perturb 
> their values.  And, the values between points are better behaved.
> 
> And making N larger to begin with doesn't affect any of this in my way 
> of looking at it.
> 
> Fred

And, I'm sure you know ..

If you use the basis 1/2 1 1/2 sum of Dirichlets (raised cosine in time) 
which I will refer to as "RC" then you do have to convolve and can't 
solve a system of equations that matches the samples exactly at each 
point.  If you did that, then it would revert to using a single 
Dirichlet I do believe.

Since the stopbands are zero then all you get in them are the 
fast-decaying tails of RC components from the passbands by 1/f^3 [rather 
than 1/f for a single Dirichlet].

Fred