[music-dsp] [faq] ola, ols and windowing

[Yaakov Stein]

> I respectfully submit (and reiterate my earlier posting) that 
> the second question is answered incorrectly). It is important to realize that, 
> mathematically, extracting a block is a time shited 

I hope that last word was a typo

> rectangular window and the spectrum of the block transform will always reflect 
> this (i.e. spectrum convolved with spectrum of the window). The use of a 
> particluar window does not change the fact that you are using OLA or OLS and the 
> outcome is entirely the same if the constant overlap add 
> constraint (and overlap save I guess) is followed. 

Just to set the record straight.

The fact that OLA or OLS extract a time segment has NOTHING
to do with windowing. It is only a programming trick to make it possible
to perform the frequency domain processing on infinite length signals.

To see this consider that the resulting output signal is EXACTLY
the same as the signal produced by the time-domain convolution,
which does ABSOLUTELY NO time-segment extraction.

This is due to the overlap operation (either on the input or output)
which precisely overcomes what would otherwise have been a
rectangular windowing operation.


> It just so happens the the COLA 

is that the drink or the spanish meaning?

> constraint for a rectangular window is a hop size of the 
> entire window! 
> I think this idea that a "block" is somehow magically separate from 
> windowing is confusing and erroneous.
> 
> Once again the process does have a name.... STFT...

STFT is the term used for performing the DFT over a limited
time window, and then shifting it over times.
Here the processing is equivalent to a time-domain convolution,
which sees the filter length at each time instant,
and advances one sample at a time.

I don't think that the term is correct here.
It IS correct for the second process mentioned in the proto-FAQ.

> 
> I think the second Q and A should be scrapped. I also think this is a 
> difficult issue to explain thoroughly without the aid of the 
> mathematical equation. 

I think that a diagram is better (who wants equations in a FAQ?)

> Is there some way we can show this in the FAQ? 
> Then it is easy to explain my point about the windows as well as the 
> filter bank interpretation of the STFT.
> 
> >A: Nope. You're talking about a different process.
> >
> I think it's the same process just with a different window as 
> explained above
> >They do not
> >window the input signal, but only cut it in fixed size blocks for
> >processing.
> >
> That's a rectangular window, so this is incorrect

see above