Inverse FFT or "Unscrambling the egg"

I know I'm missing something basic ;)
Having begun with a very long signal              ( m samples )
Done
    a fft on a series of windows n samples long  ( m >>> n )
    optionally performed some operation in the frequency domain
    done  an inverse fft on each of the modified windows

How do you "glue" things back together in the time domain?

Thank you.

On Mon, 10 Nov 2003 20:20:39 -0600, Richard Owlett
<rowlett@atlascomm.net> wrote:

>I know I'm missing something basic ;)
>Having begun with a very long signal              ( m samples )
>Done
>    a fft on a series of windows n samples long  ( m >>> n )
>    optionally performed some operation in the frequency domain
>    done  an inverse fft on each of the modified windows
>
>How do you "glue" things back together in the time domain?
>
>Thank you.
>

Richard,

   search the web for "overlap and save"
and "overlap and add".  

Good luck,
[-Rick-]
 

Rick Lyons wrote:
> On Mon, 10 Nov 2003 20:20:39 -0600, Richard Owlett
> <rowlett@atlascomm.net> wrote:
> 
> 
>>I know I'm missing something basic ;)
>>Having begun with a very long signal              ( m samples )
>>Done
>>   a fft on a series of windows n samples long  ( m >>> n )
>>   optionally performed some operation in the frequency domain
>>   done  an inverse fft on each of the modified windows
>>
>>How do you "glue" things back together in the time domain?
>>
>>Thank you.
>>
> 
> 
> Richard,
> 
>    search the web for "overlap and save"
> and "overlap and add".  
> 
> Good luck,
> [-Rick-]
>  


Dang it all, knew it must be obvious.
When is a sequence infinite?
When it's *BIGGER* than you are ;\

Now let's see if I can do it in Scilab.

P.S.
References state and/or imply that ideal ratio of input points: output 
points is 2:1 . Is that based on computational efficiency or other 
factors. I.E. would a transform on window 10x what used in output 
yield any additional "fidelity"?

"fidelity" used VERY loosely as I intend to multiply frequency domain 
components by either 1 or 0 in probably octave chunks.

Yep, phase relationships destroyed in unspecified manner.
If an implied assumption of my underlying assumptions is valid, the 
point is moot.

Thank you all for patience.