Help explaining Fourier transformation

[Kerr]

Hi all.

We had this computer lab at the university about the Fourier series and the Fourier transformation. When I got my lab back, it said I just had to explain the Fourier transformation and I would pass. Just not sure how to do it. The Fourier transformation is a complicated issue. Or rather, there is a lot to write and I don't know where to start. Does anyone have an idea? Do I need to explain the Fourier series as well to explain the Fourier transformation?

From what I remember (was a while ago I did the lab, we had a course between when I got it back and now so I haven't looked at it for more then a month):

The Fourier series is basically an infinate mathematical series with terms of the sine (or cosine) function. It turns out that every perodic function can be represented as a Fourier series (I think there are additional conditions, but that's the general idea). If you want, you can think of it as a bunch of sine terms with different frequency and amplutide that together recreates the function in question.

The Fourier transformation decomposes a function into the frequencies. Not sure how to explain it better then that, since it was a while ago. But this image I shamelessly borrow from the wikipedia page about the Fourier transformation (Fourier transform - Wikipedia, the free encyclopedia) makes it visually easier to see what happens. At least to me it does .

The red is the function, the blue iis the Fourier transformation.

Does anyone have a tip on how to explain it? Other then reading up on it again, which I will do, I'm just not good with words and asking here is faster then discussing it with the guy who reads the actual report.

Take care,
Kerr.

 

[Brickjectivity]

Shot in the dark but...

For engineering I suggest you begin by mentioning what Fourier transforms are for or what they help solve (They help to solve differential problems by changing the mathematical domain, etc.) and then express concisely your particular case. Your problem was ___ and you needed to solve ____. Why did you use Fourier in your experiment? That way if someone wants to repeat your experiment they'll be able to follow your reasoning. Did you toss it in because the instructor said to? That's unacceptable. Were there other potential ways of solving the problem? Could you have used a Laplace transformation instead? Could you have solved your problem using Euler's Ghost-Reverse-Intellectus Theorem instead? Mention alternatives if any and explain why you chose to use Fourier and how it helped. If there were no other possible methods say so.

Think of it as coming up with a prison break. Could you have done a better job if you had access to more powerful equipment? Was there some better way you could have done your whole experiment? (The answer should be 'No'. In an experiment report you are justifying your method, aka your funding.)

 

[Skwim]

As a matter of ethics, I don't think you should expect anyone else to do your assignments for you, or for anyone else to volunteer to do them. If you don't know, then so be it. Take your lumps, and next time pay attention and take better notes.

 

[Kerr]

As a matter of ethics, I don't think you should expect anyone else to do your assignments for you, or for anyone else to volunteer to do them. If you don't know, then so be it. Take your lumps, and next time pay attention and take better notes.

I don't expect anyone to do my assignments for me. Didn't want that, I just wanted guidence of how to do it. Problem is... I kind of freaked out from stress, lol. So if it sounded like I wanted someone to do it for me, sorry, wanted guidence. Could ask the teacher, but I have a lot to do and a limited time to do it, and asking the teacher takes a lot of time since it would have to be done over mail and they aren't always very responsive and so on. So I figured if I could ask for advice (not anything more) from someone who knew more about it, it might make things easier.

But I did write something. Fairly sure it's bad, I'm not good with owords. I have handed it in.

The Fourier transformation decomposes a signal or function of time, which we denote g(t), into its frequency components. Let us consider g(t) as a sum of simple sinusoidal functions of different frequencies and amplitudes. We call the Fourier transformation of g(t) for G(f). The value of G(f) relates to how powerful the frequency f is in g(t). It is a complex valued function of frequency f defined as

.... INSERT MATHEMATICAL DEFINITION HERE ...

The Fourier transformation of a signal is also called the frequency domain representation of that signal.

The discrete Fourier transform

Consider a finite list of data samples, with equal spacing. With the discrete Fourier transform, often shortened to DFT, the samples can be converted into a finite list of complex coefficients C for corresponding complex sinusoids. This list of coefficients are ordered by their frequency. A function which matches the samples can be created as a series of the coefficients and their complex sinusoids. A particular algorithm to compute the DFT is the fast Fourier transform, or FFT.

Copied this from my latex document, so i replaced the integral with "... INSERT MATHEMATICAL DEFINITION HERE...". And if you check wikipedia you can probably notice that I did write some part in a similar manner (especially the part about the discrete Fourier transform). Basically what I did was to look for places that wrote about it and tried to put it in my own words, but I'm not very good at that and I'm horribly unsure of my own understanding, so some parts sounds more similar to my sources then I would like. Not copying, though, just not good with figuring out how to write things. Did mention that I was unsure of what I wrote when I handed it in.

 

[Kerr]

Shot in the dark but...

For engineering I suggest you begin by mentioning what Fourier transforms are for or what they help solve (They help to solve differential problems by changing the mathematical domain, etc.) and then express concisely your particular case. Your problem was ___ and you needed to solve ____. Why did you use Fourier in your experiment? That way if someone wants to repeat your experiment they'll be able to follow your reasoning. Did you toss it in because the instructor said to? That's unacceptable. Were there other potential ways of solving the problem? Could you have used a Laplace transformation instead? Could you have solved your problem using Euler's Ghost-Reverse-Intellectus Theorem instead? Mention alternatives if any and explain why you chose to use Fourier and how it helped. If there were no other possible methods say so.

Think of it as coming up with a prison break. Could you have done a better job if you had access to more powerful equipment? Was there some better way you could have done your whole experiment? (The answer should be 'No'. In an experiment report you are justifying your method, aka your funding.)

Not all points are applicable, since there where no alternatives to the Fourer transformation to use (I will explain the situation bellow). But the advice to explain what they are for is very good. If the thing I sent in doesn't pass I will definately keep that in mind .

We used the Fourier transform because the experiment was specifically designed to be solved with Fourier. It didn't involve any equipment, it was a computer lab. The assignments where in the style of "we have this function, do a Fourier transform of it and plot this and that", and "make a function with a non-integer frequency, take samples and use the FFT on it and plot the resulting magnitude spectrum and explain why it looks like it does" (I think it was called magnitude spectrum at least).

The course itself was a course in optics, and then they randomly threw in a little crash course in the Fourier series and Fourier transformation in the middle (which we hadn't read anything about before at all), and then continued on with another topic. There was nothing about any Laplace transformatio or any alternative, just the Fourer transformation. And we had another lab before that I worked on so hard that when I was done I had like 1 or 2 days to read up on the Fourier transform and such before the lab. Hence why I never got a good grip on it. Tend to need to take my time to learn, instead I was thrown into an assignment and expected to figure it out as it came along, which ended up with a "very well written rapport that just needs a short introduction to Fourier transformation to pass", lol. Think a lot of the other people in my class has had similar problems, btw, so it's just not me.

I think I will add the Fourier transform to the list of things I need to actually read up on but haven't been able to because of the high rate of the courses. It will get along there with differential equations I think . Think that when I'm done with this part of my education I will try and find free standing courses in those subjects or something.