Re: finding Fourier Series.
- To: mathgroup at smc.vnet.net
- Subject: [mg63856] Re: finding Fourier Series.
- From: Bill Rowe <readnewsciv at earthlink.net>
- Date: Thu, 19 Jan 2006 00:02:58 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On 1/18/06 at 2:39 AM, bdsatish at gmail.com (bd satish) wrote:
>Which command (in MATHEMATICA) should I use to evaluate the
>so-called Discrete-Time Fourier Series ?
>Another bug: ---
>The command FOURIER[ { list } ] finds the FFT (Fast Fourier
>Transform) of a list. How can I evaluate FFT symbolically
>(instead of a numerical list ) ?
>Specifically ,
>find the FFT of a^n * UnitStep[n] , n belongs to integer
>and Abs[a] < 1
I would have answered your first question above by suggesting the use of Fourier. However, from what you written it is clear you are already aware of this command. So, it seems I don't understand what you mean by discrete time Fourier series and how that differs from what Fourier returns.
But as to your second question, the answer is FourierTransform, i.e.,
In[1]:=
FourierTransform[a^n*UnitStep[n], t, w]
Out[1]=
a^n*Sqrt[2*Pi]*DiracDelta[w]*UnitStep[n]
which can be inverted with InverseFourierTransform, i.e.,
In[2]:=
InverseFourierTransform[%, w, t]
Out[2]=
a^n*UnitStep[n]
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