Fourier Cos transform
- To: mathgroup at smc.vnet.net
- Subject: [mg123812] Fourier Cos transform
- From: Dimitris Emmanoulopoulos <demmanoulopoulos at hotmail.com>
- Date: Tue, 20 Dec 2011 03:05:44 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Hello,
I have the following question with respect to FourierDCT function.
Consider the following example
SeedRandom[34];data=RandomReal[{0,500},10];l=Length[data];
fourier = Table[1/l^(1/2) Sum[ data[[r]] Exp[2 \[Pi] I (r - 1) (s - 1)/l], {r, 1, l}], {s, 1, l}];
fft = Fourier[data];
As you expect the results from fourier and fft are the same; having of course the fft as the fastest one. Is it possible to do such a fast computation using FourierDCT or something similar for the following quantity?
cosFourier=1/(2 \[Pi] l) Table[Sum[data[[r]] Cos[2 \[Pi] r s/l],{r,1,l-1}],{s,1,l}]
Thanks a lot,
Dimitris