Harmonics

This video just has a plain transcript, not time-aligned to the videoWe can analyse signals in either the time domain or the frequency domain.
We're seeing exactly the same signal, but with different representations.
Sometimes one is more useful than the other, but most often the frequency domain is our preferred domain.
We've seen periodic signals in the time domain.
So what does a periodic signal look like in the frequency domain?
Remember, when I say 'frequency domain', I generally mean the magnitude spectrum; phase has been discarded.
Here come four speech sounds.
First, the word 'but' but spoken with a Southern British English accent (that's a bit different to my accent).
Here's just the vowel, and here's the whole word.
Now the word 'bat'; again, I'll plot just the vowel and its spectrum, and here's the whole word.
Next, a couple of unvoiced sounds.
In the upper row, both sounds are voiced; in the lower row, both sounds are unvoiced.
The voiced sounds have something in common: something that we will not find in the unvoiced sounds.
Let's take a closer look.
There's a very obvious repeating pattern in the time domain.
That's periodicity, and that gives us a distinctive line structure in the frequency domain.
See these fine lines here: we'll only find those in voiced sounds.
The energy in the spectrum is concentrated at very specific frequencies, and they're all multiples of a particular value.
I am just going to zoom in a little bit in the time domain.
We'll take a rather closer look in the frequency domain so we can see that line structure much more clearly.
In the time domain, we can see that the signal has a clear fundamental period.
In the frequency domain, we can see that the signal has energy at the corresponding fundamental frequency and at every multiple of that frequency.
Those are called 'harmonics'.
A signal that is periodic in the time domain always has harmonic structure in the frequency domain.
For speech, that applies only to voiced speech.
That's already enough information for us to construct the first component of a computational model of speech signals.
We could make an artificial sound source that has the essential properties that we've just seen.
So the next step is to find the simplest possible signal that has that property, and that will be an impulse train.