And if we plot the phase, we can also show the location

of the phases and here what is important of course are the phases in the middle.

And here we have these two pi discontinuities but basically everything

is zero, modulus two pi and it's a clear.

It's good because that means we centered the window around zero and

therefore we have what we call a zero phase window.

Okay, in order to visualize the X axis better.

Here, I typed some commands to plot it

in a way that the access are better shown.

So here what I did was to plot against an X axis array.

That has been normalized so

that the zero parting does not affect, so we divide by N and multiple by M.

So we actually see the samples, let's say of, with respect to the window and

they also have normalized the magnitude so that the maximum is zero decibels.

And I'm only plotting the values that go in the x axis from minus 22 to 20 and

the dB values, I'm plotting from minus 80 to zero.

Now, if we run this script with these lines added,

well we are seeing the magnitude spectrum of the hanning window.

But with an x axis that shows the center around zero.

And decibels starting from zero.

So now we can check the values we talked about that describe the window.

We mentioned that the main lobe.

The width of the main lobe is an important characteristic of the window.

In here we can see, if we look from the bottom

right side where our x value is of the cursor.

We can see that this main lobe sort of deep is at minus two.

And this other one is at two so clearly this main lobe at this location,

the weight is around four samples or to be called four bins.

And this is what we mentioned about the hanning window.

And then also we talked about the side lobe level, the highest side lobe level.

And here again we can put the cursor at highest side lobe level and

it tells me kind of the value that this has.

And it's around minus 31 decibels which is the kind of thing that we mention.