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If you are a physics student or an engineer, you've probably already came about through your transformers.

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If we attract Transformers are very important in several fields of physics because they can tell you

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what a periodic function consists of in terms of individual oscillations.

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So this is correct, for example, for acoustics.

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So when you have a sound and many instruments are playing at the same time, you will have a superposition

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of several periodic sine functions.

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And by calculating the full you transform off the sound, you can figure out the individual frequencies

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of the sound.

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And also, this is correct.

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For example, in electronics where you have different frequencies of your voltage in the AC scenario,

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they can use to fully transform also to decompose the individual periodic functions.

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So let's start with an example.

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Of course, we need the first num num nampai and then also we need integrals.

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This is something I can tell you already.

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So here are decided to use our integral trapezoidal methods because this is some very typical integration

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method and we will use this one in this particular lecture here as well.

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So first of all, I want to show you the superimposed function of three oscillations.

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So I create a time list, has an empty bottle in space, and we plot in the range from zero to 50 seconds

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with a step size of 500 one.

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So step size of zero point one second for the plotting.

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And then we have here three individual frequencies, which I have chosen.

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Let's use something like this frequency to will be zero point three and frequency three will be three

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point five.

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And now we can calculate a whitelist list, which will be two values.

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And this will be a superposition of periodic functions with these frequencies.

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So, for example, we can use now as zero point five times and predict cosine t list times frequency

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one.

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And then similarly, we use plus another amplitude 2.0 times and P Dot Cosine.

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We could also use to sign function.

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It wouldn't really matter.

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T list times frequency two.

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And then the last one will be 1.0 times and putative cosine t list times frequency three.

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And now our data will be the composition out of these two arrays and three.

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And then, as I just said, composition T list and why list.

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And we will plot the data by using multiple live and calling data zero and data one.

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So this is really nothing new, of course, and this is what we'll get.

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We have to time on the x axis and we have to value of the signal at the y axis.

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This could, for example, be some sound that is recorded, which is the superposition of three individual

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frequencies.

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And now let's see.

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This is our dataset that we have that we have measured and we want to figure out what are these frequencies

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of these individual oscillations.

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So say we forget about these numbers and we only have this data set here.

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How do we figure out what are the frequencies?

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Of course, we could now go ahead and fit individual cosine functions, and we, as I said, we could

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also change the face here, for example, at just a number.

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Change this one to sign.

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And the signal will look a bit different then, but the frequencies will be the same in this case.

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So for fitting the signal, we would first need to figure out that these are three individual frequencies.

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And then we would have to fit the three frequency parameters and the three faces, which would be which

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could be different for the three individual oscillations.

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So this would be quite difficult.

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And I can tell you that actually we are going to do this later on in one of the exercises.

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And one of the later sections of this course, but it's actually much easier to just call the four year

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transform.

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Just as a test before we do this, I can show you that we can just call our integral trapezoidal methods.

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Sorry, a typo here trapezoidal.

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And then just call our data.

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This is why I have written it down like this so that we could not just integrated and the integral basically

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of this function with respect to the x axis is eleven point three seven three.

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But that doesn't help us at all figuring out what are the frequencies for this we need to fully transform.

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And the four year transform is based on an integral part.

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It's a bit different.

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We do not just integrate over data, but we need an additional factor.