Is "brick wall" filter realizable?

eric.jacobsen@ieee.org (Eric Jacobsen) wrote in message news:<4154bafa.61193656@news.west.cox.net>...
> On Fri, 24 Sep 2004 17:38:57 -0500, Richard Owlett
> <rowlett@atlascomm.net> wrote:
> 
> >glen herrmannsfeldt wrote:
> >
> >> 
> >> 
> >> Richard Owlett wrote:
> >> 
> >>> This is intentionally "dumb" question.
> >>> I suspect a good answer will illuminate a fallacy in my thinking.
> >> 
> >> 
> >>> assume a real input
> >>> perform FFT
> >>> set all bins to 0 that are outside pass band
> >>> perform suitably scaled IFFT
> >> 
> >> 
> >>> What's wrong with this picture?
> >> 
> >> 
> >> It is as sharp as the number of points in the transform.
> >> (The frequency resolution is 1/(total length of transform).)
> >> 
> >> You need an infinite number of points for an infinitely
> >> sharp cutoff.
> >> 
> >> -- glen
> >> 
> >
> >Caution: I'm learning DSP by asking questions on this group
> >
> >I had gotten the impression there was another problem other than what 
> >may be considered "resolution issues'.
> 
> You can implement a filter that way, and sometimes it's a fine thing
> to do.   Another thread here mentioned how this was used successfully
> in some data processing, but subsequent use of a FIR with a sharp (but
> not infinite) cutoff worked better.

Well, there are two problems with 'brick wall' filters. First, the 
frequency responses are determined only at a finite number of 
frequencies, with the magnitude response left unspecified in between.
Second, the transition band is exactly one frequency bin wide, which 
is un-necessary sharp in most situations, and causes extensive ringing
in time domain. 

Whaich is the reason why one started using windowed FIR filters in the 
first place: The filter lengths are specified in terms of the allowable
transition bands, and ripple is specified over the full band.

Rune

Richard Owlett wrote:

(snip)

> In my case I'm starting with speech recorded on CD under studio 
> conditions. I assume the signal was suitably low pass filtered before 
> sampling. I will playback the filtered signal using the original sample 
> rate. Would that make the effect moot or not?
> 
> I doubt I'll would do a true "brick wall" but it is a worst case limit 
> of what I might do.

I have wondered in past discussions how long it takes to do
an FFT of a whole CD.   The filter can't be sharper than
1/(length of data), but for a 60 minute CD that is about
  0.0003Hz, close enough to brick wall for most of us.

-- glen

Richard Owlett wrote:

> This is intentionally "dumb" question.
> I suspect a good answer will illuminate a fallacy in my thinking.
> 
> assume a real input
> perform FFT
> set all bins to 0 that are outside pass band
> perform suitably scaled IFFT
> 
> What's wrong with this picture?

Thank you one and all.
I've learned at least one thing.

If wandering lost, ask about "degenerate" (spelling?) case.
Responses will point out fallacious logic.