       Re: FFT in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg113686] Re: FFT in mathematica
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Mon, 8 Nov 2010 03:36:36 -0500 (EST)
• References: <ib38tv\$f2k\$1@smc.vnet.net>

```On 06/11/10 09:59, Gazi Habiba Akter wrote:
> Hi,
> I don't understand how fft algorithm works.
> but i have to solve a problem by Mathematica code .I am not math and
> physics student it need my thesis work.
> it will be ok if any body explain by a simple function.
> .I tried to solve this problem using fourier transform in mathematica
> directly but it does not work.I think i need to modify my function or
> need to know how FFT works for my problem. Here is my code
> ClearAll["Global'*"]
> z = 0;
> n = 100;
> v1 = 0.5*(1 + Tanh[n*t]);
> x = (2*t (1 + z))^0.5;
> v2 = Hypergeometric1F1[.5, 1, -2 x];
> v3 = Exp[x - t];
> r1 = v1*v2*v3;
> f = FourierTransform[r1, t, v];
> w1 = InverseFourierTransform[f*Exp[z/2*(1 - I*v)], v, t]
>
> I need the plot of w1 with respect to t for different value of Z. here
> r1 is only for z=0.
> it will be great for me if anybody help me.
> Thanks,
> rupa
>
The Fast Fourier Transform (FFT) operates on discrete data (a list of
numbers), and the output is another list of (usually complex) numbers.
The function Fourier performs a fourier transform on discrete data, and
if the length of that data is a power of 2, it is able to get the result
faster using the FFT, rather than a slower algorithm.

You have a symbolic expression - not a list of data - so either you need
to create a table of values of your function, or do as you are now, and
work with the symbolic FT.

You might also want to check with your course tutor as to what you are
supposed to be doing!

David Bailey
http://www.dbaileyconsultancy.co.uk

```

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