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Robert E. Beaudoin wrote:
" <r...@sens.com> wrote in message news:<e08a9$41366e86$44a72252$2...@msgid.meganewsservers.com>...
> U-CDK_CHARLES\Charles wrote:
> > On Wed, 01 Sep 2004 18:55:09 +0200, Andor Bariska <a...@nospam.net> wrote:
> > 
> >>Charles wrote:
> >>...
> >>
> >>
> >>>...and in fact a function can be continuous ONLY at x_0.
> >>
> >>That doesn't make sense. If a function is continuous in x_0, it is also 
> >>continuous in a small open interval containing x_0.
> >>
> > 
> > 
> > Ah . .right.  I mangled that bit.
> > 
> 
> Let f(x) = x if x is rational, and f(x) = -x if x is irrational.  Then
> f is continuous at 0 but discontinuous everywhere else.  Now back to
> your regularly-scheduled DSP programming....
> 
> Bob Beaudoin

Nice one. I could have sworn ... :-)

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In article <1...@corp.supernews.com>, r...@atlascomm.net wrote:

>When I've said an "arbitrarily shaped function" {be it time or 
>frequency domain} my only implied restriction was that it be 
>continuous ( would 'smooth' be better term).

If you dig into the Parks-McClellan code, you can hack it to produce any 
frequency response shape you want as a function of frequency.  You can also 
modify the weight function to encourage more precision in different portions 
of the frequency domain.  You wind up throwing away a lot of the code having 
to do with generating the frequency response and weighting by bands but it is 
quite ease to do.  

You are limited to specifying the frequency response and weighting at discrete 
frequencies not continuously. And of course, the number of frequencies is 
limited to a hundred points or so.

An easier method is to specify the complex frequency response at equally 
spaced points in frequency domain and doing a complex to real inverse DFT.  
The real output of the DFT are the FIR filter tap weights that provide that 
frequency response.

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George Bush wrote:

> In article <1...@corp.supernews.com>, r...@atlascomm.net wrote:
> 
> 
>>When I've said an "arbitrarily shaped function" {be it time or 
>>frequency domain} my only implied restriction was that it be 
>>continuous ( would 'smooth' be better term).
> 
> 
> If you dig into the Parks-McClellan code, you can hack it to produce any 
> frequency response shape you want as a function of frequency.  You can also 
> modify the weight function to encourage more precision in different portions 
> of the frequency domain.  You wind up throwing away a lot of the code having 
> to do with generating the frequency response and weighting by bands but it is 
> quite ease to do.  
> 
> You are limited to specifying the frequency response and weighting at discrete 
> frequencies not continuously. And of course, the number of frequencies is 
> limited to a hundred points or so.
> 
> An easier method is to specify the complex frequency response at equally 
> spaced points in frequency domain and doing a complex to real inverse DFT.  
> The real output of the DFT are the FIR filter tap weights that provide that 
> frequency response.

Provided you window the coefficients get adequate stop-band attenuation.
That's not different from flat-topped filter design.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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I'm not sure I understtand your comment, Jerry.  You might want to add a 9 
point cosine taper at the upper end of the band if you have a significant 
weight there but that is all that comes to mind.

In article <413a74ef$0$19710$6...@news.rcn.com>, Jerry Avins 
<j...@ieee.org> wrote:
>George Bush wrote:
>
>> In article <1...@corp.supernews.com>, r...@atlascomm.net wrote:
>> 
>> 
>>>When I've said an "arbitrarily shaped function" {be it time or 
>>>frequency domain} my only implied restriction was that it be 
>>>continuous ( would 'smooth' be better term).
>> 
>> 
>> If you dig into the Parks-McClellan code, you can hack it to produce any 
>> frequency response shape you want as a function of frequency.  You can also 
>> modify the weight function to encourage more precision in different portions 
>> of the frequency domain.  You wind up throwing away a lot of the code having 
>> to do with generating the frequency response and weighting by bands but it is
> 
>> quite ease to do.  
>> 
>> You are limited to specifying the frequency response and weighting at
> discrete 
>> frequencies not continuously. And of course, the number of frequencies is 
>> limited to a hundred points or so.
>> 
>> An easier method is to specify the complex frequency response at equally 
>> spaced points in frequency domain and doing a complex to real inverse DFT.  
>> The real output of the DFT are the FIR filter tap weights that provide that 
>> frequency response.
>
>Provided you window the coefficients get adequate stop-band attenuation.
>That's not different from flat-topped filter design.
>
>Jerry

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George Bush wrote:

> I'm not sure I understtand your comment, Jerry.  You might want to add a 9 
> point cosine taper at the upper end of the band if you have a significant 
> weight there but that is all that comes to mind.
  ...

FIR filter coefficients obtained by transforming the desired frequency 
response to the time domain represent only a part of the theoretical 
impulse response; the rest is truncated. A window function applied to 
those coefficients improves the stopband attenuation. If there is no 
stop band, my remark may not apply.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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