Fourier Transform as a Function of Frequency w Versus Frequency f (in Hertz)
A slecture by ECE student Randall Cochran
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
To show the relationship between the Fourier Transform of frequency $ \omega $ versus frequency $ f $ (in hertz) we start with the definitions: $ X(w)=\int\limits_{-\infty}^{\infty} x(t)e^{-jwt} dt \qquad \qquad \qquad \qquad X(f)=\int\limits_{-\infty}^{\infty}x(t)e^{-j2\pi ft} dt $
now we let $ \omega $ = 2$ \pi $$ f $
$ X(2\pi w)=\int\limits_{-\infty}^{\infty} x(t)e^{-j2\pi ft} dt /math> ---- ---- ---- (create a question page and put a link below) ==[[slecture_title_of_slecture_review|Questions and comments]]== If you have any questions, comments, etc. please post them on [[slecture_title_of_slecture_review|this page]]. ---- [[2014_Fall_ECE_438_Boutin|Back to ECE438, Fall 2014]] $
