So now let's put it out together into an analysis

synthesis system using this Stochastic model.

And as of here we see the blog diagram that we will be implementing

which we start from the signal x of n, hopefully an Stochastic signal.

We compute the FFT.

We take the absolute value.

And then we do this Stochastic approximation which is again,

this idea of low pass filtering.

So approximating the magnitude spectrum with a smooth curve.

And then we can do the synthesis.

The synthesis will be done by doing this inverse FFT of

this stochastic approximation that might have to be zero path and

so to interpolated to be a longer size spectrum,

and then we generate random numbers for the phase spectrum.

And we can take the inverse FFT of that and

that will return a fragment of a sound.

And then we can just do an overlap at

the similar in this exact the same way that we did for the sinusoidal modelling.

Here also we will have to take care about some smoothing windows so

that they overlap at works correctly but,

with these we can reconstruct the original signal.

So, let's listen to some example okay, so,

this is the ocean sound that we played before then,

the first is the magnitude spectrum, the absolute value of the spectrum.

Of the spectrogram of this whole sound with a particular window and

50 size and a size.

And then the Stochastic approximation is basically

a visualization of this coefficient that are much fewer.

So in fact here we took a kind of compression of point so,

I've written samples of our magnitude spectrum,

we reduced it to one so, that's the idea of the approximation.

And then, we can synthesize by combining these

magnitude spectrum with random numbers.

So let's listen to

the synthesize result [NOISE].

If you do an AB comparison with the original ocean,

it sounds different but it clearly sounds like an ocean sound.

So, for stochastic symbols, maybe it's not relevant to reproduce

the exact characteristics of the sound but basically this

kind general characteristics of the sound and this is what this approach does.