Periodic signal

This video just has a plain transcript, not time-aligned to the videoThe most important source of sound in speech is the periodic vibration of the vocal folds.
Here's a reminder of the two principal sources of sound when producing speech.
Now let's introduce some engineering terms to describe their general properties.
On the left we have voicing.
That's the phonetic term: voicing means the vibration of the vocal folds and that results in a periodic signal.
Periodic signals are predictable.
You could continue the plot on the left and tell me what happens next.
We call this type of signal 'deterministic'.
On the other hand, frication results in a signal that has no periodicity: it's very unpredictable.
So we could say that that is 'aperiodic' or 'non-periodic'.
(They mean the same thing.)
Aperiodic signals are not predictable.
You cannot guess what happens next in the plot on the right.
So we could use some engineering terms.
Periodic signals are 'deterministic': we know what happens next.
Aperiodic or non-periodic signals are 'stochastic': we don't know what happens next, they're random.
Periodic signals are so important, we're going to take a closer look now.
All periodic signals have a repeating pattern.
In this particular signalm it's really obvious what that repeating pattern is.
We can also see exactly how often it repeats: every 0.01 s or 1/100th of a second.
We can use some notation to denote that.
We use the term T0 to denote the fundamental period.
T0 has a dimension of time and a unit of seconds.
Here we can see what T0 is.
It's the time it takes for this signal to repeat.
Here's another signal.
This is a very special signal called a sine wave.
This one has a fundamental period of 0.1 s or 1/10th of a second.
So if we repeated this cycle 10 times, we'd fill up a duration of exactly 1 s.
Another way of talking about the signal is, instead of saying that the fundamental period is 0.1 s, we can say that it has a fundamental frequency of 10.
We'll use the notation F0 to denote fundamental frequency, and that's just going to be equal to 1/T0.
But what are the units of frequency?
10 is the number of periods per second and the units of time are seconds.
The units of frequency are 1/s (1 over seconds) or, in scientific notation, 'seconds to the minus 1'.
That's a little bit of an awkward unit.
Since frequency is so important, we don't normally write down this unit, which we could say out loud as 'per second'.
We give it its own units of Hertz.
These are all equivalent.
The scientific unit of frequency is Hertz.
But just remember, it always means precisely the same as '1 over seconds' or 'seconds to the minus 1'.
The old fashioned unit of frequency was actually very helpfully called 'cycles per second', but we don't use that anymore.
So what are the fundamental periods and the fundamental frequencies of these signals?
Sit down and work them out while you pause the video.
I hope you remembered to always give the units.
In the top row, we've got 10 cycles in one second.
So that's a fundamental period of 0.1 s and we've got then an F0 of 10 Hz.
I hope you got that right, with the units.
Top right, we've got a fundamental period of 0.01 and that gives us a frequency of 100.
But always write the units!
T0 = 0.01 s and F0 = 100 Hz.
Down on the bottom left, we've got a much higher frequency signal.
That's got a fundamental period of 0.0005 s and then it's got a fundamental frequency of 2000 Hz.
We could now use some more scientific notation because once we're into the thousands we could start saying a multiplier for the Hz.
Instead of writing 2000 Hz, we could write 2 kHz.
Those are the same thing.
Bottom right, it's a little bit trickier.
This is a speech signal, but it's pretty obvious what the fundamental period is here.
We can see a clear repeating pattern, and it's going to be from here to here, and so T0 is pretty close to 0.005 s to give us an F0 of 200 Hz.
Periodic signals are very important as a sound source in speech.
Thinking about speech perception and about getting a deeper understanding of speech as a means of communicating a message, we'll find that periodic signals are perceived as having a pitch, or a musical tone, and that can be employed by speakers to convey part of the message.
Pitch is part of a collection of other acoustic features that speakers use, which collectively we call prosody.
Thinking on the other hand about signal processing and about getting a deeper understanding of speech signals, for example, so we can make a model of them, we're going to need to move out of the time domain and into the frequency domain where will see that this very special periodic nature in the time domain has an equally-special, distinctive property in the frequency domain, and that is harmonics.