I’m a bit late, but your discussion reminded me of this paper:

        I. Kauppinen and K. Roth, “Audio signal extrapolation - theory and 
applications,” Proc. of the 5th Int.         Conference on Digital Audio 
Effects (DAFx- 02), 2002. 

The idea is to extrapolate in time-domain using autoregressive process model. 
Each sample is modeled by

        x(n)= ∑a_k * x(n−k)

with {a_1, a_2, ..., ap} being the AR coefficients. The AR coefficients can be 
identified by system identification algorithms like the Burg algorithm. 
Basically to extrapolate W samples based on ns past known samples:

• Identify the AR coefficients by using the Burg algorithm
• Initialize the filter with ns past known samples just before the section to 
be extrapolated
• Feed zeros of length W into the filter

The quality of the extrapolation can be very good, even though this is 
computationally quite expensive. 

I’ve reimplemented it in python: 
        https://github.com/faroit/freezefx

Also have a look at this notebook for some audio examples:      
        
http://nbviewer.jupyter.org/github/faroit/pyfreeze/blob/master/freeze_demo.ipynb


> On 16 Sep 2016, at 21:59, Emanuel Landeholm <emanuel.landeh...@gmail.com> 
> wrote:
> Simple OLA will produce warbles. I recommend a phase vocoder
> 

Compared to OLA or FFT based methods, the AR model extrapolation sounds quite 
natural (especially when using higher filter orders). 

Cheers
Fabian
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