Impulse train

This video just has a plain transcript, not time-aligned to the videoWhen viewed in the frequency domain, all periodic signals are revealed to have harmonics.
In speech, the only periodic sound source is the vibration of the vocal folds, which we call 'voicing'.
Our destination is a model that can generate speech.
So now we're going to devise a sound source for voiced speech and we know the key property that it must have.
It needs to contain energy at the fundamental frequency - that's called F0 - and at every multiple of that frequency, so that we have the harmonics.
It's going to play the part of the vocal folds in our eventual model of speech.
So let's devise a signal that has the correct harmonic structure.
It's going to be an impulse train.
In fact, we already came across this signal when we talked about the vocal folds as a source of sound.
All we really need to do is to confirm that, indeed, it has energy at every multiple of the fundamental.
Here's the signal.
This is the time domain, so this is a waveform.
We can see that this signal has a fundamental period of 5 ms.
The other way of describing that is to say that it repeats 200 times per second, so it has a fundamental frequency of 200 Hz.
Let me plot the magnitude spectrum of this signal.
It looks like this.
That confirms indeed that there is energy at the fundamental frequency, which is 200 Hz, and it every multiple of that, 400, 600, and so on forever, at least up to the Nyquist frequency.
Also notice that there is an equal amount of energy at each of those multiples of F0.
But you shouldn't just take my word that this is the right signal.
Whenever you come across any scientific or engineering decision, whether it's made by you or by somebody else, you should always ask yourself, 'What are the alternatives?'
So let's consider some alternative signals to the impulse train, to see if any of them would be better.
They all need to be periodic.
So how about the very simplest periodic signal there is, the sine wave?
Well, the sine wave certainly has energy at the fundamental frequency, but it has energy only at the fundamental frequency, by definition.
It's a pure tone; that's not suitable.
We need energy at all of the harmonics to give the harmonic structure that we see in voiced speech; so that's not suitable.
There are lots and lots of other periodic signals.
We could make, instead of an impulse train or a sine wave, we could make a square wave.
A square wave is periodic, but this only has energy at the odd multiples of the fundamental: at the 1st one, 3rd, 5th and so on.
That's not suitable because in natural voiced speech, we see energy all the multiples, so a square wave wouldn't be useful either.
We could look across many, many other periodic signals.
How about this one, called the saw tooth waveform?
That looks a bit more promising.
That has energy at every multiple of the fundamental frequency.
But it doesn't have an equal amount.
There's a decaying amount of energy at each of those.
In our eventual model, there is going to be another component responsible for deciding how much energy there is in each of the harmonics.
For now, we just want the simplest possible signal.
This is not the simplest possible one.
We're going to go with the impulse train because it has energy at every multiple of the fundamental, and it has an equal amount of energy.
So, it's the simplest possible signal.
The impulse train is, then, the first essential part of the model that we're working towards.
The model is called the 'Source Filter Model'.
We're going to take this impulse train and we're going to pass it through a filter.
By filtering this very simple sound, we're going to make speech sounds.
Then we'll be synthesising speech with a model!
Whenever that model needs to generate voiced speech, the source of sound will be an impulse train.