Question

(Fourier Series) I'm confused as to why in the Mathematica documentation on Fourier Series, when you specify a coefficient you want it to solve for, it doesn't let you specify the bounds to evaluate it-how are you supposed to get a fourier coefficient without using bounds given to do so?!?

http://reference.wolfram.com/language/ref/FourierCoefficient.html

Answer 1

(e.g. bounds to specify the periodicity of the given function, I don't see a place to specify the period)

Answer 2

im currently being hacked right now!

Answer 3

Sometimes I find it really hard to like you, dan. I'll talk to you later.

Answer 4

@Kainui

Answer 5

ok lets see

Answer 6

they are using complex representation of the fourier series, can u write that out

Answer 7

Yeah, either complex or trig, that's not what I'm asking about; I'm saying in the general form I don't see where the bounds are to establish the period of the function.

Answer 8

Alright, great, looks like he's not getting "Hacked!" anymore.

Answer 9

Yeah, I just don't see in the documentation how you can specify the period of a function, I see that you can specify the function itself, the variable of the given function, and the number of coefficients.

Answer 10

@Kainui , do you get what I'm saying.

Answer 11

I think I do, but I'm not sure. Can you give me an exact example of something you'd like to compute as an example so I understand what it is you want that you think you won't be able to receive?

Answer 12

Let's say the Fourier series of x, where -pi<x<pi.

You need -pi and pi obviously to compute it.

Answer 13

It looks like you'll need to change the settings here http://reference.wolfram.com/language/ref/FourierParameters.html Honestly I am not very familiar with Mathematica, but I understand what you're interested in finding.

Answer 14

Fourier Parameters refers to the Fourier Transform.

Answer 15

I looked at that, too, thinking that was it, but it says in the heading that it's for the transform.

Answer 16

Gotta go to an exam, I'll talk to you later, and thank you, nonetheless.

Answer 17

Yeah good luck, I have no clue as far as Mathematica is concerned, sorry.

Answer 18

@phi

Answer 19

the coefficients are found by integrating from 0 to T , where T is the period of your periodic function... or any lower bound to upper bound that represents the period.
It looks like mathematica assumes -pi/2 to +pi/2

Answer 20

Alright, so if you want to specify a bound that is different from -pi/2 to pi/2, you just need to use the Integrate [f(x),x] command?

Answer 21

And find the coefficient separately from using the FourierSeries commands?

Answer 22

What I'm trying to do is check my work for Fourier Series where there isn't a listed answer (my book has almost no answers, I'm okay with no solutions, but no answers makes everything kind of massively useless).

Answer 23

actually, it looks like {1,1} is the default
and they say that means -pi to +pi

Answer 24

Wait, what? I didn't understand that. Can you change the default, or not? I couldn't figure it out from looking at the documentation,

Answer 25

You can tweak it

Answer 26

what exactly are you trying to check?

Answer 27

I think I figured out something that should partly do the job, if anybody interested comes across this: http://classes.engineering.wustl.edu/jemt3170/Mathematica%20-%20Fourier%20Series.pdf

I'm taking a look at what you put, too.

The problem with the FourierParams things that I don't understand is that there isn't an example with the FourierSeries command, only ones for the Fourier Transform.

Answer 28

Do you have Mathematica, or no? I really need to find someone who has this and knows how to use the software in general.

Answer 29

Now I just have more questions on top of the old ones.

Answer 30

Do you or do you not have Mathematica/have you used it a ton? it's absolutely fine if you haven't, I just want to know to think about what I probably can or cannot get.

Answer 31

I have used Matlab, and Sage (does stuff similar to mathematica, but its openware)
I assume you did the example on page 5
It shows using the FourierParams

Answer 32

I can ask them in a separate thread if you want me to, but I have a bunch of questions relating to mathematica. On the document I just posted, I don't understand how the integrals on the second page or so at the top-in integral form and all, not code-are listed as input.

How the hell did they get that as input? That makes no sense to me, that looks exactly like output.

Answer 33

My main goal here is not numerically calculating a fourier series to a certain number of terms, but finding the general coefficients in a fourier series for a given term over a given period

Answer 34

Talking about this: http://i.imgur.com/vW4nvAn.png

Answer 35

In[4], In[7], and In[8]

Answer 36

Can you duplicate the stuff on page 1 ?

Answer 37

Yeah, do you want me to? I don't understand how that would help with the page 2 stuff, but I'll definitely do it, one moment. And I'm also confused about the random gaps in between the input and output numbers, e.g. Out[4] to In[7]

Answer 38

I'm not sure why, but I got this: http://i.imgur.com/e2Jd6Uf.png

I'll check out the very end now

Answer 39

I got a garbage page for the letter L, I think a link was bad or something.

Answer 40

extra comma

Answer 41

But what about the weblink? I'll fix the extra comma, but I got this for the webpage: http://i.imgur.com/obZmmfo.png

Which I'm guessing is exactly not what you intended

Answer 42

no, I'm working on it. It's a pdf file I am trying to link to

Answer 43

Alright, replicated everything in the first page

Answer 44

now do In[4]
I assume you have to type it as 1/(2*Pi) Integrate[ f[x] ...

Answer 45

I hope so, one sec.

Answer 46

Also, thank you so much for your help so far, this has been comparatively really productive.

Answer 47

What should I do about a_0 in In[4]? I haven't defined it and it doesn't appear to...oh well

Answer 48

I think you type a0= ?

Answer 49

This is what I did, and it was wrong, it looks like a O lowercase, so I'm not sure why it would be a0 instead of ao

Answer 50

http://i.imgur.com/PjKL4jB.png

Answer 51

they are just evaluating the first coefficient (which uses a different formula than for a1, a2, ...)
I would try
In[]:= x= 1/(2*Pi) Integrate(f[x], {x, -Pi, Pi} )

Answer 52

It says in the Mathematica documentation that a b and a*b are identical, but I'll try that

Answer 53

make that x[t], {t, -Pi, Pi}

Answer 54

It didn't like the parentheses, and when the parentheses were changed to brackets, it didn't work: http://i.imgur.com/ZWkgSjA.png

Answer 55

In[]:= a0= 1/(2 Pi) Integrate[ x[t], {t, -Pi, Pi} ]

Answer 56

One sec

Answer 57

Also the In[] stuff always shows up regardless of what you do, I don't believe it needs to be written, I don't think

Answer 58

No, it types the In[]:=
but I assume you would not type that part.

Answer 59

(Lol, I wasn't sure, I was assuming you wouldn't put that in there then, my bad)

Answer 60

Partial success, it did evaluate correctly, but it evaluated immediately and didn't give me that input that looked like an integral and all that jazz in formal math rather than code; the good news is, I can at the very least do stuff, what I don't understand from the written code is how it knows what x[t] is, in my mind that's literally just like f(x), it's not a function, it's just the general notation for one

Answer 61

Hey, I think I might've figured it out

Answer 62

x[t] was still defined when you did the page 1 stuff

Answer 63

It might have to do with this: https://reference.wolfram.com/language/tutorial/FormsOfInputAndOutput.html

http://reference.wolfram.com/language/tutorial/ExecutingNotebookCommandsDirectlyInTheFrontEnd.html

Answer 64

I know it somehow "delays" something, but I didn't understand what the difference would be in the first page had I left out the underscore in defining x, I mean, immediately thereafter I executed and got the graph, how would leaving the underscore out change things?

I also can't thank you enough for this, this is a good conversation and I'm learning a lot at least about Mathematica.

Answer 65

I interpreted the t_ in x[t_] to mean x is a function of t, with t not yet being assigned a value.

Answer 66

For what its worth, here is the fourier series stuff

Answer 67

And had it been assigned a value, how would that change things? I'll go plug in otherwise, but I don't understand how with the graph at least it would've changed anything, nor how or when t was assigned a value.

I'm not a programming person at all so I don't really know what I'm talking about, but how/when did we assign t a value, in the computer's eyes?

Answer 68

t gets assigned when you typed in {t, -Pi, Pi} inside the integrate operation

Answer 69

Alright, cool.

I couldn't really interpret the stuff about the kernel and all, but did you figure out/see how to put the input like that? If not, it doesn't really matter at all, I can still do the exact same thing functionally, and that's what matters.

Answer 70

the "front-end" you are typing into can be a notebook. you would have to figure out how to start up the notebook

Answer 71

Alright, cool. Thanks for the help!