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how to solve  Fourier Series on maple ??

I have computed the eigenfunction expansion for f(x)=x on 0<x<1 in terms of the eigenfunctions exp(-x/2)*sin(n*Pi*x).

I wish to calculate the weighted L2 error in this expansion (the weight function is w(x)=exp(x)).

Specifically, I want to determine how many terms in the eigenfunction expansion are necessary for the error to be less than say 0.3.

Here is the code:

f := x -> x
w := x -> exp(x)
assume('n', integer);
y :=  (n, x) -> exp(-x/2) sin(n Pi x)       
c := n-> (int(f(x)*y(n, x)*w(x), x = 0 .. 1))/(int(y(n, x)^2*w(x), x = 0 .. 1))
Fourierf := (n, x) -> sum(c(j)*y(j, x), j = 1 .. n)

fsolve(Lerror(n) = 0.3, n);

This seems to run forever without giving a value of n.  I know this is a large computation, but it seems that Maple should be able to handle it.  Does anyone have any suggestions?

Heather

 

Hi

 

I want to write the functional Z of J Z = exp(Int(Int(J(x)*Delta(x-y)*J(y), x), y))with Delta(x) = Int(I*exp(-I*k*x)*(1/(k^2-m^2)), k) in terms of the fourier transform of J: J(x) = Int(J(p)*exp(-I*p*x), p).

Actually I'm in Minkowski space and all the integrals should be over 4 dimensions, x,y,k,p should all be four-vectors, but I wanted to keep things short. (The only way I have found to express a 4D integral is using Physics-Intc with the singleparameters of the four vector. Is there a more convenient way to get d^4x?) But still in 1D I cannot solve it.

To find the solution, an exponential of only one integral, is actually pretty easy, since there are integrals over e. g. exp(-I*x*(p-k)) deliver a delta distribution, but I cannot reproduce this in Maple since he doesn't perform the integral over x.

I have found that I can/have to use the command inttrans-fourier to gain the delta distribution, but when I try to use it for the problem mentioned above I run into all kinds of problems. Not to mention that I cannot manage to perform a fourier transformation in 4D.

Does anybody know how to solve this problem? Thanks!

Hi all,

 

I have recentry constructed Fourier amplitude and Fouier Power graphs which are plotted against the frequency of the oscillations, like the picture below.

 

I would like to change the frequency scale along the x axis into a period scale in order to Fourier analyse future ODE systems in  terms of period rather than frequency.

But I unsure how to manipulate my code to do so.

 

Any help would be much apreciated, and the Maple file that I am using is attached.

 

Thanks in advance!

 

Fourier_with_Period.mw

 

 

Hi All,

 

Where can I download Fourier Series Package? I found other posts related to this but the link is not working.

 

Thanks.

 

Hi,

 

I was wondering how to go about plotting a Fourier Tranform in Maple.

My assignment is to plot a simple harmonic equation as a Fourier transform, depicting amplitude against fequency.

I've been given: x'' + w^2 x = 0

And want to obtain both the f(x) = a0 sin(wt) + b0cos(wt) form, and a graph of the the amplitude (c^2 =a0^2 + b0^2) against frequency.

I know how to do this on paper but not in Maple, so any help with line commands and layout would be very much appreciated.

 

Thanks

If I do even expansion for the function 2*x-2, x from [0,1], to the real line,how do I make Maple to produce

the Fourier cosine expansion in the form 2*x-2=a_0/2+Sum(a_n cos n*Pi*x)

 

?

 

hi

how can I download Fourier series package?

Does Maple have any tool or package that computes the Fourier & Fourier-Bessel series expansions of a given funtion "f(x)" over a specified interval "[a,b]"?

Below is the function that I have.

 

f := (t-1)^(1/3)

p:=2;

b[n] := 2/p*(Int(f*sin(2*Pi*n*t/p), t = 0 .. p))

 

I also included a picture below to show what it is doing. Some help would be greatly appreciated. All I need to know is why maple doesn't want to evaluate bn?

 

Maple Code

 

Using the Fourier convolution theorem to solve f(t) =sin (t)

f(t)=R dJ(t)/dt+J(t)/C

Hi,

Maybe someone can give me a nice answer without Maple.

I am given a fourier series:
ln|cosx|=Co - sum( (-1)^k/k * cos2kx,k=1..infinity)
and am asked what this tells me about the chevychev series for ln(u).

 

Thanks

I am trying to get a Fourier transform of a Gaussian:

so I say

and get

The Fouriertransform of a Gaussian is well known and the result I expect is something like

exp(1/2*sigma^2*omega^2)

ignoring normalizations & other factors. I know that I can add functions to inttrans, but I kind-of expected inttrans[fourier] to know how to transform a Gaussian, it is a commonly used transformation. Even if I set phi0 to 0 it does not produce anything useful.

???

Mac Dude

Hello, I am trying to do a fourier transfrom using the package < DiscreteTransfroms >.

The function is an gaussian function for now,

Here is the code I tried

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

restart

with(DiscreteTransform):

> X := Vector(1000, proc (k) options operator, arrow; (1/200)*k-5/2 end proc);
> Y := Vector(1000, proc (k) options operator, arrow; evalf(exp(-10*((1/100)*k-5)^2)) end proc);

> X2, Y2 := FourierTransform(X, Y);
Vector[column](%id = 18446744080244879358),

Vector[column](%id = 18446744080244879478)
> plot(X2, Re(Y2));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The program returns two vector, X2 and Y2 who are supposed to be the fourier transforme of a gaussian so.. a gausian but when I plot the result X2 on the horizontal and Y2 on vertical, the graph doesn't resemble a gaussian function or any function at all.

 

Please help!!

Alex

Find the Fourier Series for the function f(x) defined as follows, and compare the graphs of some truncated Fourier series (try 1,2,3,5,6,30, terms) with the graph of f(x).

 

f(x)= min(|x|, pi/2), -pi less than or equal to x less than or equal to pi.

 

Also, let f(x) be periodic with a period of 2*pi. Thanks.

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