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
fft and the derivative
2 messages · Todd Remund, 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. ---------------------------------------------------------------------------- ------- 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 ---------------------------------------------------------------------------- -------- -----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 ______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.