let's use the same values that we use before, 1024 for

both FFT size and window size with the blackman window.

And we can compute, okay, and this is basically what we saw before.

This is the 1024 samples we have started with, this is the magnitude and

phase spectrum and we see clearly the peaks corresponding to the harmonics.

I mean, here we see the phase spectrum, which we didn't see before, and

also we see the inverse of this.

So, this is the windowed signal that we generate back

by taking the inverse FFT of this spectrum.

And, of course, we can do the same thing.

We can change windows, for example,

if we change the window size to 256, and also the 50 size to 56.

In the same location, we compute, well,

we see we are, of course, taking much less samples and

the spectra are much smoother, less information there, okay?

One advantage, of course, with this interface we have is that we

can independently control the window size from the FFT size.

So we can put FFT size 1024 and

maybe a window size not that large, maybe 801.

It will compute, okay?

We are taking less samples than before but

still the frequency resolution is quite good.

And it's quite smooth because we have been doing zero padding and

so the shape of the spectrum is quite nice.

Okay, let's look at all these from the short-time Fourier transform

perspective from the spectogram.

So we will get the same sound.

Okay, and again, let's put 1024, 1024 and

the hop size has to be at least much smaller than the window

size in a way that they overlap at factor as correctly.

So for 1024 in the blackman window, at least we need one-fourth.

So let's put 256 and we compute.

Okay, and this is the result.

So we have the input signal.

The magnitude spectrogram, the phases

of the time-varying phases and the output sound and the output sound.

[SOUND] Well, it's very much the same than the original because we

have done a good reconstruction with a good overlap.

However, if this overlap is not correctly set for

example, let's put the same than the windows size for

example, 1024 and let's compute it.

Well, clearly now is something wrong in the output signal and

if we can listen to it [SOUND], okay?

Of course, we see this modulation that is at the frame rate because

we are not overlapping correctly, so every frame we see a burst of sound,

and they don't balance out by the overlap factor.

So we definitely need to have a much smaller hop size.