Then we saw that these sinusoidal,

these harmonic components of sounds do not capture everything in the sound.

There is a part of the sound that is left out, and

this is the residual or it's the overcasting component.

So when we have analyzed the sinusoids of the harmonics of the sound

We can actually subtract them from the original sound and obtain residual,

that is what is left and is sometimes quite relevant.

Sometimes that's a very small part of the sound that can be discarded,

so it's not perceptually relevant.

But in many cases,

this is an important part of the sound that needs to be preserved.

It needs to be captured.

And we can just capture ICTs and that will need to residual component or

we can modulate with the stochastic model, with the idea of filtered white noise.

So in the bottom, a representation the residual is approximated with

this idea of a time bearing filter, Through which we put white noise.

So we have this complete model of Sinusoidal plus stochastic components,

and that captures many sounds.

Not all the sounds are properly modeled this way.

But, quite a large family of sounds either sinusoidal plus stochastic or

harmonic plus stochastic can be used to model many sounds.

And that then yields many potentials for

capturing the essence of the sound or being able to modify the sound.

And that what brought us to the idea of transforming sounds.

When we have these type of representations We have these harmonics or

these sinusoids.

And we have the frequencies, the amplitudes, and the faces, and

they can be processed.

They can be manipulated quite a lot.

We can change quite a bit their values, and the stochastic component too.

And things like time is stretching or a shift in the frequencies or

doing arbitrary changes.

In fact, in the class we went over some common transformations, but

there are many more that we could do that go beyond what we cover in class.