0:53

Let's hear it.

Â [SOUND].

Â Okay.

Â In order to see that it's periodic, we can zoom into it,

Â and here we see the sinusoid oscillation, the periodic oscillation of a sine wave.

Â If we zoom even more, we are going to start seeing the samples

Â that are present in this signal, this discreet signal.

Â So we have generated this signal at 44,100 hertz, so

Â we'll have that many samples per second.

Â Okay, so the first thing we might want to do to understand

Â the concept of periodicity is to measure what is the period length.

Â Now the idea of periodic means that there is

Â a period that is repeating a cycle of the sound.

Â Okay, so this is a cycle of this sinusoid,

Â and in here we can see what is the length of this selection I made.

Â And it says that it's 0.002.

Â So that means 2 milliseconds.

Â If we go to the terminal and have Python in, we can use it as a calculator.

Â So we can convert this period length into frequency.

Â So the inverse of the period, so

Â 1 over 0.002, will be our frequency.

Â And of course it gives us 500 hertzs.

Â 500 hertzs is the frequency of this sinusoid.

Â Okay, another thing we might want to check is okay,

Â this period has a series of sample.

Â So, how many samples does one period of this sinusoid has?

Â Well, in order to compute that, what we should do is start with the sampling rate.

Â The sampling rate is 44,100.

Â And multiply by the duration of this period.

Â So we multiply by 0.002.

Â And it gives me 88.2,

Â which is the number of samples of a period.

Â Of course it should be an integer number.

Â So I guess it's going to be 88 samples in one period, okay?

Â Now let's generate another sinusoid but of a different frequency.

Â So let's maybe open a new file, okay?

Â And let's create another sinusoid.

Â But instead of 500 hertz, let's put, for example, 5000 hertz.

Â Okay, so this is the sinusoid of 5000 hertz.

Â We can hear it too.

Â [SOUND].

Â Clearly, much higher, and we can also zoom,

Â and to see the periodicity.

Â But here we already see that is not so nice, in fact

Â the samples are not really shaping a smooth sinus little function.

Â This is because there is less samples per period,

Â therefore we don't have a various most version.

Â So how many samples are in one period?

Â Well, not that many.

Â In fact, here we can even count them.

Â And it's one, two, three, four, five, six, seven, eight.

Â So in fact we have like eight, nine samples for one period.

Â Not exactly because they don't coincide, of course, with a period.

Â Of course it makes sense because if we had seen that

Â the frequency of Pythagorean had 88 sample in one period.

Â Now that we have 10 times the frequency, 5,000, the number of samples

Â will be 10 times less, so it's going to be around 8 or 9 samples, that's pretty good.

Â Of course, this relationship between the number of samples and

Â the frequency is a very important one, and related with the sampling rate.

Â The bigger the sampling rate, of course, more samples we'll have.

Â And for higher frequencies, we'll have more samples.

Â At 44,100, as we go up in frequency, and if we go even higher,

Â like 10,000 or even 15,000, the number of samples will be very less.

Â And therefore,

Â the shapes will not look like a sinusoid even though it's a sinusoid.

Â 6:27

But in this case, the period which we can measure and

Â it's going to be the same thing, 500.

Â It doesn't mean that there is one frequency at 500 hertz.

Â In fact, this wave form has many frequencies.

Â It has 500 hertz as a fundamental frequency and it has multiples of that.

Â So that it's a harmonic sound.

Â And how can we check that?

Â Well, we check that with a spectrum analysis.

Â And in Audacity, we have specifically to plot the spectrum, okay?

Â And here now it tells me that there is not enough data because I have to choose

Â a bigger part of the sound, so let's choose a bigger fragment of the sound.

Â And now we can plot, now we can visualize the spectrum of this shuttle.

Â And clearly we see that is a quite complex spectrum, in which it has many peaks.

Â In order to understand this,

Â I think it's good to compare it with the sinusoidal we started with.

Â So this was the sine wave we started.

Â And if we do the same thing that we have done now with the status, that is to

Â compute the spectrum, well we see now that it's clearly very different.

Â The spectrum of a sinusoid has only one measure peak.

Â And the frequency in this case, 400.

Â And the spectrum on this has many peaks

Â which correspond to all the frequencies present in this harmonic signal.

Â 8:54

So now we have kind of a glissando, a chirp, and of course we can play it again.

Â [SOUND].

Â Okay, so it's a frequency that goes up, and again of course, we can zoom.

Â But we will see that the period keeps changing in time.

Â So here at the beginning,

Â we'll have a period that is going to be quite long.

Â It will be the 500 hertz, the 2 milliseconds.

Â And by the end, it will be much smaller.

Â It will be ten times smaller, okay?

Â And of course we can visualize that by analyzing the spectrum of this signal.

Â So if we select a portion at the beginning and analyze the spectrum,

Â we will see that it has around 500 hertz frequency.

Â And if we go to the end, so we go to

Â 10:47

And we have talked about electronic periodic signals,

Â synthesized periodic signals.

Â These are signals that are quite good to play around with because we know how we

Â generate them, so therefore when we analyze them we know what to expect.

Â So in next demo class, we'll complicate that, so

Â we will actually analyze more complex signals, sounds, that might

Â have some parts of the periodic, might have some parts that are not periodic.

Â So they reflect more the reality of real sounds, so

Â I hope to see you next class, thank you very much.

Â