Why don't we just zero out FFT bins?

On Fri, 10 Apr 2009 02:08:18 -0700 (PDT), Rune Allnor
<allnor@tele.ntnu.no> wrote:

>On 10 Apr, 02:17, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:
>> On Thu, 09 Apr 2009 08:22:55 -0500, "bmh161" <bmh...@yahoo.com> wrote:
>
>> >Instead of going through all the trouble of designing complicated digital
>> >filters, why don't we just pick the frequencies that we want to supress and
>> >replace those bins in the FFT with zeros?
>...
>> &#4294967295;I just wanted to say that
>> your question is sensible and that we, the DSP guys here,
>> should investigate the process of freq-domain filtering
>> in detail
>
>Rick, did we read the same post? The question is not why
>frequency domain filtering is a bad idea, but why one doesn't
>use the naive, 'obvious' specs for the filters. I commented on
>a similar question not too long ago:
>
>http://groups.google.no/group/comp.dsp/msg/2d4bd5dfb25b5a23
>
>Such questions are covered in most DSP texts - I wouldn't be
>surprised if you touched on the subject already.  If not, the issue
>might be worth half a page's comments in your 3rd edition, as
>your book is the first entry point into DSP for lots of users.
>
>Teachning students how to think 'right' is an admirable (and
>difficult!) task; warning against how to think 'wrong' can only
>help the effort.
>
>Rune

Hi Rune,
   Oh shoot.  Maybe I misunderstood the poster's 
question.  For whatever reason, I thought he was 
asking: "Can we perform an N-point FFT on an N-point 
time sequence, zero-out the spectral components 
that we wish to attenuate, and then perform an 
N-point inverse FFT to obtain a "filtered" 
time-domain sequence.  

If the original poster was asking about ways to 
design a time-domain digital filter, then I 
completely missed the point of his question.
(That wouldn't be the first time for me.)
 
[-Rick-]
PS. Rune, I wish you "calm seas."

On Fri, 10 Apr 2009 08:13:48 +0200, "Robert Lacoste"
<see-alciom-dot-com> wrote:

>
>"bmh161" <bmh161@yahoo.com> a &#4294967295;crit dans le message de 
>news: -9CdnboVQ4Mya0DUnZ2dnUVZ_vednZ2d@giganews.com...
>> This is probably a stupid question but, well, I'm not all that smart...
>>
>> Instead of going through all the trouble of designing complicated digital
>> filters, why don't we just pick the frequencies that we want to supress 
>> and
>> replace those bins in the FFT with zeros?
>>
>
>Doing what you propose (FFT of the signal, multiplying with a frequency 
>mask, IFFT) gives EXACTLY the same result mathematically speaking than a FIR 
>filter, its just another way to calculate it. In a nutshell :

   [snipped by Lyons]

Hi Robert,
   are you sure about that?  Let's say I have a 
1024-sample time sequence on which I perform a 1024-pt 
FFT.  Next, I zero-out the FFT bins (samples) for the 
freqs I want to attenuate.  Finally I perform a 1024-pt 
inverse FFT.  My resultant "filtered" time sequence 
is 1024 samples in length (just as was the original 
time sequence).

Now ...what kind of time-domain digital filtering can 
I perform on the original 1024-sample time sequence 
where the  filter output sequence is EXACTLY the same 
1024 samples as the above freq-domain filtering output?
I believe the answer is: "There *IS* no such time-domain 
digital filter."

As far as I know, the freq-domain filtering I discussed in 
my first paragraph above is equivalent to time-domain circular 
convolution, and time-domain filtering does 
not perform circular convolution.

Robert, if I'm mistaken, then I'd sure like to 
know about it.

See Ya',
[-Rick-]
 

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=9B UTC+8=E4=B8=8B=E5=8D=889=E6=99=8222=E5=88=8655=E7=A7=92=E5=AF=AB=E9=81=
=93=EF=BC=9A
> This is probably a stupid question but, well, I'm not all that smart...
>=20
> Instead of going through all the trouble of designing complicated digital
> filters, why don't we just pick the frequencies that we want to supress a=
nd
> replace those bins in the FFT with zeros?

You may be interested in the simple experiment using matlab.

https://poweidsplearningpath.blogspot.com/2019/04/dftidft.html