Continuous-Time Fourier Transform 1.1 2004/06/10 16:47:24 GMT-5 2004/06/29 13:34:16.013 GMT-5 Richard G. Baraniuk richb@rice.edu Harika Basana ilsai@rice.edu Richard G. Baraniuk richb@rice.edu Jeffrey Silverman jsilv@rice.edu Per Thorsteinsson s001552@student.dtu.dk Introduction to the continuous-time Fourier Transform. Theme: Fourier representation for infinite-length "aperiodic" signals

Fourier Series

Fourier Transform

Alternative notations for CTFT: F ω and F ω Recall that Fourier Series builds up periodic or finite length signal from sum of harmonic sinusoids with frequencies that are multiples of ω o 2 T CTFT builds up arbitrary signal from sum of sinusoids of all frequencies ω F ω t f t ω t f t 1 2 ω F ω ω t CTFT is totally symmetrical except for the 1 2 goes with δω Alternate normalizations include : 1 2 in both the above equations. Do not use rad/sec frequency ω but rather Hz frequency γ . Then all the 1 2 's go away.