Signal Interpolation

On 2004-11-03 17:08:44 +0100, Andor Bariska <an2or@nospam.net> said:

> Stephan M. Bernsee wrote:
>> To do this right you need to do the same backwards in time from the end 
>> of the missing segment and blend the sinusoidal parameters between the 
>> two sets. Then you'll have to sort out ambiguity (what oscillator at 
>> the beginning of the gap corresponds to which one at the end)... this 
>> can be fairly complicated it you want to do it right.
> 
> There is no need to do that - one can just crossfade the (forwards and 
> backwards) oscillator outputs.

Not sure if that's enough... imagine a singer singing a note at slowly 
increasing pitch. If you simply crossfade between the two segments 
you'll hear a glitch. If you track the pitch across the gap and match 
the oscillators you get the correct result...
-- 
Stephan M. Bernsee
http://www.dspdimension.com

Andor Bariska wrote:

> Bernhard Holzmayer wrote:
> ...
>> build a new FFT signal where at every frequency bin newFFT=min(FFT1,FFT2)
> 
> What's the min of two complex numbers?

Right, should have been more precise.
Since it's a real audio stream, I guess that optimal phase response isn't 
so important as long as the loudest portions are suppressed.

I'd probably solve it for the real parts. 
With the imag parts? - Either do the same, or just average the two values.
I don't know which is more appropriate.

I guess, it's more important for the OP to find a quick and dirty solution
which provides an agreable result, than to identify an optimal algorithm.

Bernhard

On 2004-11-04 08:21:11 +0100, Bernhard Holzmayer 
<Holzmayer.Bernhard@deadspam.com> said:

> I'd probably solve it for the real parts. With the imag parts? - Either 
> do the same, or just average the two values.
> I don't know which is more appropriate.

I still don't get it - what exactly are you trying to do?
-- 
Stephan M. Bernsee
http://www.dspdimension.com

Stephan M. Bernsee wrote:
> On 2004-11-03 17:08:44 +0100, Andor Bariska <an2or@nospam.net> said:
> 
>> Stephan M. Bernsee wrote:
>>
>>> To do this right you need to do the same backwards in time from the 
>>> end of the missing segment and blend the sinusoidal parameters 
>>> between the two sets. Then you'll have to sort out ambiguity (what 
>>> oscillator at the beginning of the gap corresponds to which one at 
>>> the end)... this can be fairly complicated it you want to do it right.
>>
>>
>> There is no need to do that - one can just crossfade the (forwards and 
>> backwards) oscillator outputs.
> 
> 
> Not sure if that's enough... imagine a singer singing a note at slowly 
> increasing pitch. If you simply crossfade between the two segments 
> you'll hear a glitch. If you track the pitch across the gap and match 
> the oscillators you get the correct result...

That's true - as I wrote originally, one needs the assumption of (local) 
stationarity of the signal for the algorithm to work. For short 
drop-outs (< 20 samples), this is generally ok. For longer stretches (as 
in a slowly increasing pitch section), this becomes a problem.

The next step would be to try to find a non-stationary model, such as 
ARIMA or fractional ARIMA or something else. Highly non-trivial.

Regards,
Andor

On 2004-11-04 10:07:35 +0100, Andor Bariska <an2or@nospam.net> said:

> That's true - as I wrote originally, one needs the assumption of 
> (local) stationarity of the signal for the algorithm to work. For short 
> drop-outs (< 20 samples), this is generally ok. For longer stretches 
> (as in a slowly increasing pitch section), this becomes a problem.
> 
> The next step would be to try to find a non-stationary model, such as 
> ARIMA or fractional ARIMA or something else. Highly non-trivial.
> 
> Regards,
> Andor

Yes I agree. Clearly, most of the problems of DSP techniques (at least 
in the area I'm working in) come from the assumption of short-time 
stationarity, which is a helpful concept to begin with but can't be 
ignored if you really need very high-end stuff...
-- 
Stephan M. Bernsee
http://www.dspdimension.com