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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]"?

I need to know if the Software Maple solve, step-by-step series of Fourier and Laplace transforms? The Maple command has to solve step by step series of Fourier and Laplace transforms? or commands show only the direct solution?

Below is the function that I have.


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


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


I've been instructed to create an animation showing the changing plots of a single square waveform using 5,10,20,40,80,160,320, and 640 terms in my Fourier series. This is my code right now: 


with (plots):
L := [seq(2^i, i = 0 .. 6)];

[1, 2, 4, 8, 16, 32, 64]

animate( plot, [2/((2*n-1)*Pi))*sin((2*n-1)*Pi*x], n=L);
Error, `)` unexpected


It doesn't work. Can anyone explain what I'm doing wrong, or how to solve my question?

I want to do a step by step computation for obtaining the coefficents of the sine fourier series expansion of f(x)=x over the interval [-L,L]. The steps are as follows:

1-write the fourier expansion as: Sum(A[n]*sin(n*pi*x/L),n=1..N)
2-multiply the series by: sin(m*pi*x/L)
3-integrate the series over the interval [-L,L]
3-using the orthogonality properties of the set {sin(n*pi*x/L} compute the A[n].

I can't do these steps since I have problem with the series manipulations in maple!
Can any one suggest a way from begining to the end?

Thanks. :)
Below shows what I did in Maple 17.

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

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


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).




I open a discussion about convolution and Fourier coefficients in Fourier series.


I have a function defined by f(x)=0 if x in [-Pi,0[ and 1 if x in [0,Pi[, of course f 2*Pi periodic function.

My goal is compare the Fourier coefficients of f*f ( * convolution ) and The Fourier Coefficient of f.


Thanks for your help.




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


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




> 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!!


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.


I would like to ask maple to "recognize" a Fourier transform in a (possibly complicated) expression.

Maple defines a Fourier transform in this way:
convert(fourier(f(x), x, k), Int);

So if f(x)=1 we should get something that is proportional to Dirac(k), which we do:
fourier(1, x, k);

...but given an expression
exp1:=Int(exp(-I*x*k), x = -infinity .. infinity);

... how would tell...

construct a vector with entries of symmetric real parts and anti-symatric imaginary parts,such as v:=<1+2I,5+3I,9+4I,9-4I,5-3I,1-2I>;DiscreteTransforms[FourierTransform](v);By property of fourier transform,the result should be real numbers,but it is not this. Imaginary parts not vanish

Maple gives the fourier transformation:

fourier(int(y^k*exp(-k*x*y/phi+I*y*omega), y = 0 .. infinity), omega, t) as:

2*Pi*t^k*exp(-t*k*x/phi)*piecewise(t < 0, 0, 1)+piecewise(0 < t, -2*Pi*t^k*exp(-t*k*x/phi), 0)

but it is identically 0.

if change the order of integration and integate exp(I*y*omega) first, the transform is equal to

int(Dirac(y-t)*y^k*exp(-k*x*y/phi), y = 0 .. infinity)

which is Heaviside(t)*t^k*exp(-t*k*x/phi)

I want to know how to take the fourier transform of a solution to an IVP obtained using dsolve/numeric and consequently plot the transform. any ideas?


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