[R] fft and the derivative

[Ravi Varadhan]

Todd, 

Your idea is correct for "continuous" Fourier transform, but I am not sure
how one could apply that to fft, which corresponds to the discrete Fourier
transform.  For instance, what values of omega would you use for the term
"i*omega" to get the discrete fourier transform of the derivative of f(t)?  

Ravi.

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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

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-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Todd Remund
Sent: Monday, June 25, 2007 5:16 PM
To: r-help at stat.math.ethz.ch
Subject: [R] fft and the derivative

Can one take f(t) and transform to F(omega) in the frequency domain using 
fft(), and use the properties of the fft and find the derivative of f(t)?  
For example,

f(t) <-> F(omega) => f(t)^n <-> (i*omega)^n  *  F(omega)

Use this and get,

f(t)^n = F^(-) [ (i*omega)^n  *  F(omega) ]

to get the nth derivative of f(t)?
Todd Remund

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