FFT vs. Fourier transform

Hey guys,

I'm stuck with this http://postimage.org/image/745s4qbub/

The top graph is the function is wish to get the spectrum of

The middle one is what I find via a Fourier transform integral i.e. integral f(t)exp(iwt)dt

And the last one is my results via the FFT routine...why is this so??

Answer 1

[Daniel Shub]

When dealing with Fourier analysis, you need to be careful with terminology. The fast Fourier transform (FFT) is an efficient implementation of the discrete Fourier Transform (DFT). There is also the discrete-time Fourier transform (DTFT) which under some stimulus conditions is identical to the DFT. There are also continuous time Fourier transforms.

You seem to be comparing a continuous-time Fourier transform (your integral) with a discrete-time Fourier transform. It is not surprising to me that you are getting different results.

Steve Eddins addressed these issues nicely in his blog a few years ago: (see blog posts starting on Novermber 23 2009):

http://blogs.mathworks.com/steve/category/fourier-transforms/