So in the previous lecture, we finished our task and we have accomplished the intensity spectrum where
we had this pronounced peaks here at zero point three, two and three point five, which were indeed
the characteristic frequencies that we have used for the superposition of two three oscillators or the
periodic functions that we have used in the beginning to create this periodic signal here.
By the way, one thing that I didn't really mention here is that for the boundaries, for the integration,
according to the formula, we would have to use minus infinity to positive infinity.
However, here I've just used zero to 50, and you see, still it worked.
So it isn't really that important to use here to correct range, which you can never really do, but
because you can't do go to infinity.
So basically, it's OK to just use what you have.
And now the purpose of this lecture, which will be a very short lecture, is to show you that while
our methods is fine for our purposes and we will use it in the following lectures, there's even a faster
way to calculate before you transform.
And for this, we can use the non-paid module, which is called AMP Dot 50 50.
So it's called a fast food.
You transform methods.
So I will not explain to you how it works.
This is just a code, how you can use it, and you see there's just a single command here off the white
list and then you can just plotted and you're finished and you just need to rearrange a bits.
The result and then you get the result again.
And you see there's a peak at zero point three, two and three point five by you using exactly this
method here.
So it gives you the correct results, but the difference is that it's faster and that it accounts for
the data that we feed to the signal.
So you have to think of it like this when our data is not continuous, which it never is, there is
always the step, size and the data, then you can never have frequencies that are faster than or that
have shorter periods than the step size that we provide.
And this is used here by fast food to transform to consider only the frequencies that are even allowed
by the step size.
Sounds a bit difficult, but I think we don't really have to bother with this.
Just remember, you can use just for your transform and it gives you the correct results.
But I think for educational purposes, it's totally fine to use ORF3a transform.
I don't think it's much nicer to use the function that we have just programmed in the following.