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So in the previous lecture, we finished our task and we have accomplished the intensity spectrum where

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we had this pronounced peaks here at zero point three, two and three point five, which were indeed

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the characteristic frequencies that we have used for the superposition of two three oscillators or the

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periodic functions that we have used in the beginning to create this periodic signal here.

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By the way, one thing that I didn't really mention here is that for the boundaries, for the integration,

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according to the formula, we would have to use minus infinity to positive infinity.

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However, here I've just used zero to 50, and you see, still it worked.

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So it isn't really that important to use here to correct range, which you can never really do, but

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because you can't do go to infinity.

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So basically, it's OK to just use what you have.

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And now the purpose of this lecture, which will be a very short lecture, is to show you that while

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our methods is fine for our purposes and we will use it in the following lectures, there's even a faster

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way to calculate before you transform.

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And for this, we can use the non-paid module, which is called AMP Dot 50 50.

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So it's called a fast food.

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You transform methods.

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So I will not explain to you how it works.

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This is just a code, how you can use it, and you see there's just a single command here off the white

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list and then you can just plotted and you're finished and you just need to rearrange a bits.

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The result and then you get the result again.

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And you see there's a peak at zero point three, two and three point five by you using exactly this

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method here.

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So it gives you the correct results, but the difference is that it's faster and that it accounts for

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the data that we feed to the signal.

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So you have to think of it like this when our data is not continuous, which it never is, there is

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always the step, size and the data, then you can never have frequencies that are faster than or that

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have shorter periods than the step size that we provide.

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And this is used here by fast food to transform to consider only the frequencies that are even allowed

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by the step size.

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Sounds a bit difficult, but I think we don't really have to bother with this.

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Just remember, you can use just for your transform and it gives you the correct results.

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But I think for educational purposes, it's totally fine to use ORF3a transform.

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I don't think it's much nicer to use the function that we have just programmed in the following.