Frequency domain notch filter

>Hi Skaggio,
>Here is a link for a simple recursive filter that does what you want.  
>
>http://www.dspguide.com/ch19/3.htm
>
>If you want to construct a more powerful frequency domain filter, you
need
>to read the design procedures in these two chapters.  
> 
>http://www.dspguide.com/ch16.htm
>http://www.dspguide.com/ch17.htm
>
>Regards,
>Steve
>
Ok.
I will print and read them. I hope ch16 and/or ch17 will help me to
understand why removing a bin corresponds to a sync convoution in time
domain. I associate sync convolution in time to low pass filter or to rect
in frequency... It is clear I must to look over base theory again...
See you next monday!

Kind regards,
Ska

"skaggio" <andrea.scaggiante@gmail.com> wrote in message 
news:_5Wdneu3-oQomgfanZ2dnUVZ_qelnZ2d@giganews.com...
> >When you do something in the frequency domain you also have to take
>>into account the causality of it in the time domain. You are
>>essentially performing a brickwall filter, which leads to the ringing
>>due to time domain aliasing - the infinite sinc() get wrapped around
>>into your ifft block/time series.
>
> Dave, is it possible to say I got lost? I'm missing understanding about
> sinc. sinc? Why sinc? Where's the rect I don't see in this filtering?

The temporal extent NT is a rectangular window if you don't otherwise 
window.  Where N is the number of samples and T is the sample interval.

The frequency extent fs is a rectangular window if you don't otherwise 
window.  Where fs=1/T and the frequency resolution is fs/N or 1/NT.

The Fourier Transform (and Inverse) of a rectangular window is a sinc.  The 
wider the window the narrower the sinc and the narrower the window the wider 
the sinc.
For a temporal rectangular window of length NT, the distance between the 
zeros of the sinc in frequency is 1/NT - the same as the frequency sample 
interval.
For a frequency rectangular window of length fs, the distance between the 
zeros of the sinc in time is T - the same as the time sample interval.

Now, if you zero pad to make the sequences longer then these relationships 
no longer hold and the sincs are narrower / the samples are closer together.

Fred

Fred 

>
>"skaggio" <andrea.scaggiante@gmail.com> wrote in message 
>news:_5Wdneu3-oQomgfanZ2dnUVZ_qelnZ2d@giganews.com...
>> >When you do something in the frequency domain you also have to take
>>>into account the causality of it in the time domain. You are
>>>essentially performing a brickwall filter, which leads to the ringing
>>>due to time domain aliasing - the infinite sinc() get wrapped around
>>>into your ifft block/time series.
>>
>> Dave, is it possible to say I got lost? I'm missing understanding
about
>> sinc. sinc? Why sinc? Where's the rect I don't see in this filtering?
>
>The temporal extent NT is a rectangular window if you don't otherwise 
>window.  Where N is the number of samples and T is the sample interval.
>
>The frequency extent fs is a rectangular window if you don't otherwise 
>window.  Where fs=1/T and the frequency resolution is fs/N or 1/NT.
>
>The Fourier Transform (and Inverse) of a rectangular window is a sinc. 
The 
>wider the window the narrower the sinc and the narrower the window the
wider 
>the sinc.
>For a temporal rectangular window of length NT, the distance between the

>zeros of the sinc in frequency is 1/NT - the same as the frequency sample

>interval.
>For a frequency rectangular window of length fs, the distance between the

>zeros of the sinc in time is T - the same as the time sample interval.
>
>Now, if you zero pad to make the sequences longer then these
relationships 
>no longer hold and the sincs are narrower / the samples are closer
together.
>
>Fred
>
>Fred 
>
Ok.
Now I'have got a really better picture about the issue.
Thanks a lot to everyone partecipated to his thread.

Kind regards,
Ska

>>Now, if you zero pad to make the sequences longer then these
> relationships
>>no longer hold and the sincs are narrower / the samples are closer
> together.
>>
>>Fred

I re-read what I wrote here and decided to make it clearer.

If you zero pad to make the sequences longer then these relationships still 
hold and the sincs remain the same as before zero padding.  It's a little 
more complicated than that but not much!

At the same time, there is a *new* sinc that matches the new length with the 
zeros added.  It's related to the "apparent resolution" that it seems you 
have with the longer zero-padded sequence - the apparent resolution results 
from interpolation of the original samples.  It doesn't really add any 
information - but maybe a much nicer picture if you're looking at filter 
frequency response (as one example).

Fred 

On Jan 28, 2:51 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:
> >>Now, if you zero pad to make the sequences longer then these
> > relationships
> >>no longer hold and the sincs are narrower / the samples are closer
> > together.
>
> >>Fred
>
> I re-read what I wrote here and decided to make it clearer.
>
> If you zero pad to make the sequences longer then these relationships still
> hold and the sincs remain the same as before zero padding.  It's a little
> more complicated than that but not much!
>
> At the same time, there is a *new* sinc that matches the new length with the
> zeros added.  It's related to the "apparent resolution" that it seems you
> have with the longer zero-padded sequence - the apparent resolution results
> from interpolation of the original samples.  It doesn't really add any
> information - but maybe a much nicer picture if you're looking at filter
> frequency response (as one example).
>
> Fred

The way I like to think about this is that there is
a Sinc associated with the original rectangular window
on samples taken.  This Sinc doesn't get any narrower
in absolute dimensions with any zero stuffing or other
interpolation unless you widen the original rectangular
window by taking more actual data samples.

The apparent increase in resolution without adding more
actual data is just zooming in more accurately on the
shape of this original Sinc function (or the sum of a
bunch or them), which is already known (or can be
interpolated using narrower Sinc's).


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M