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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.

Hi:

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?

 

Dear All,

I am trying to find the exact amplitude and phase angle for the signal, with values attached using MATLAB.  BUT the phase angles doesn't make sense.  Can you guys help me in doing the FFT of the signal and find the amplitude and phase using MAPLE.   I am interested in,  fundamental component, 5th , 7th , 11th, 13th 15th, 17th and 19th harmonics with their phases.

I shall be very thankful if anyone of you can actually solve the problem.

The sollowing sum S is a Fourier series of a non constant function. But the Maple result is a constant value of the function hypergeom. That can't be true.

 

S:=Sum((-1)^(1+k)*cos(2*Pi*k*x)/(-1+16*Pi^2*k^2), k = 1 .. infinity);

S=value(%);

Greetings,

I have a finite Fourier series of the form, Asin(x)cos(z) + Bsin(2x)cos(z) + Csin(3x)cos(2z) +... I would like to be able to extract the coefficients, A,B,C etc., that correspond to a specific mode. I have tried using the coeff and coeffs functions. They work for a one-dimensional Fourier series (i.e. if S= Asin(x) + Bsin(2x) + Csin(3x); is my series, then coeff(S,sin(2x) returns B). I cannot however get this to work for the 2-D case. Any suggestions?

refer to Madan's paper about VG in year 1998

equation (6)

tm := int(expand(1/(rho*sqrt(2*Pi*g))*exp(-((X-theta*g)^2)/(2*g*rho^2))*g^(t/v-1)*exp(-g/v)/v^(t/v)/GAMMA(t/v)),g=0..infinity);
characteristicfun := invfourier(int(tm,x=0..infinity),x,w);

it is not equal to (1/(1-i*theta*v*u+(v/2*rho^2)*u^2))^(t/v) ?

it can not be calculated

Hi,

I would like to know if there are any command that can generate the first n terms of the fourier series expansion of a piecewise continuous function ( and/or its odd/even extensions). I am looking for a command similar to what the taylor( ) command does for Taylor series.

I found some references on packages such as "OrthogonalExpansions" and "Fourier" none of which are avaliable with a standard Maple installation. If user-defined packages are my only option,...

The fourier transform of a signal results in an answer with Real and Imaginary parts.

When I want to plot those results, is it correct that I need to take sqrt(Re^2 + Im^2)  ? 

However, if I just plot the Real parts of the answer why is that not correct?  Of course half the answer is missing, the imaginary part? but since it's imaginary it's not really that real and so why should it be included? 

Can someone shed some quick light on that subject for me? 

Hi,

I would like to calculate the inverse fourier transform from this: 

fourier(laplace(g(x, t), t, s), x, k) = exp(-s*`&tau`-I*Zeta*k)/(s+a^2*k^2)

And I get this:

I  Presented problems for the plot "DB magnitude spectrum."
The structure of vector data spec has the following configuration,Float (-infinity), inside.

N := 64;
T := 1;

f := .25;
A := 1;
phi := 0;
n := Vector(N, -> i-1, datatype = complex[8]);

x := cos~(2*Pi*n*f*T);

X := DiscreteTransforms[FourierTransform](x, normalization = none);...

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