Fourier Transform

[thelegitrohan]

Hello everyone! I needed some help on how to conduct a Fourier transform on these waveforms. I'm in high school so I've got only a slight idea about how these things work and I needed to understand this concept for a project I'm doing so some explanation would be greatly appreciated. As far as I know, this function can be written as sin and cosine waves. Thanks!

 

[Romsek]

So you want us to type out what is generally going to be at least one or two classes on the Fourier transform.

Go ask your teacher for help. They should be able to point you to a mini-tutorial on the Fourier transform.

 

[thelegitrohan]

So you want us to type out what is generally going to be at least one or two classes on the Fourier transform.

Go ask your teacher for help. They should be able to point you to a mini-tutorial on the Fourier transform.

Yeah well I tried asking my teacher and she really didn't know much about it and I've already watched a crapload of videos on the subject. I'm not really asking for a super thorough explanation, just the answer and how to get there.

 

[Romsek]

How did you generate those graphs? You have a file of samples?

You can't do a Fourier Transform as such on an array of samples.

What you can do is called a Discrete Fourier Transform and you have some options about how to go about it.
You can take all your data at once and transform it. You can break it into pieces if you think the frequency content is time varying.
Looking at your signals they appear to be the sum of a few sine waves with a bit of noise so I'd transform the whole chunk at once.

Do you have any software available? I think even Excel will do a DFT for you these days. Mathematica, Matlab, Maple, etc. certainly will.

For completeness this is the formula for a DFT on an array of \(\displaystyle N\) samples, \(\displaystyle x_0,x_1,\dots, x_{N-1}\)

[MATH]X_n = \sum \limits_{k=0}^{N-1} x_k \exp\left(\dfrac{-i 2\pi }{N}n k\right),~n = 0,\dots, N-1[/MATH]
There are better ways to calculate it though.

 

[thelegitrohan]

How did you generate those graphs? You have a file of samples?

You can't do a Fourier Transform as such on an array of samples.

What you can do is called a Discrete Fourier Transform and you have some options about how to go about it.
You can take all your data at once and transform it. You can break it into pieces if you think the frequency content is time varying.
Looking at your signals they appear to be the sum of a few sine waves with a bit of noise so I'd transform the whole chunk at once.

Do you have any software available? I think even Excel will do a DFT for you these days. Mathematica, Matlab, Maple, etc. certainly will.

For completeness this is the formula for a DFT on an array of \(\displaystyle N\) samples, \(\displaystyle x_0,x_1,\dots, x_{N-1}\)

[MATH]X_n = \sum \limits_{k=0}^{N-1} x_k \exp\left(\dfrac{-i 2\pi }{N}n k\right),~n = 0,\dots, N-1[/MATH]
There are better ways to calculate it though.

I used an application called Audacity which records sound waveforms. Suppose I were to use excel, how would I go about it? Thanks for all the help so far by the way.