Discrete-Time Fourier Transform Properties 2.5 2000/07/18 2004/08/09 11:13:56.444 GMT-5 Don Johnson dhj@rice.edu CJ Ganier seejaie@rice.edu Don Johnson dhj@rice.edu Mariyah Poonawala mariyah@rice.edu Prashant Singh prash@ece.rice.edu Fourier Transform Discrete-Time Discrete-Time Fourier Transform properties Sequence-Domain Frequency Domain Gives various Fourier transform properties

Discrete-Time Fourier Transform Properties Sequence Domain Frequency Domain Linearity a1 s1 n a2 s2 n a1 S1 2f a2 S2 2f Conjugate Symmetry sn real S 2f S 2f Even Symmetry sn sn S 2f S 2f Odd Symmetry sn s n S 2f S 2f Time Delay s n n0 2 f n0 S 2f Complex Modulation 2 f0n sn S 2 f f0 Amplitude Modulation sn 2 f0n S 2 f f0 S 2 f f0 2 sn 2 f0n S 2 f f0 S 2 f f0 2 Multiplication by n n sn 1 2 f S 2f Sum n sn S 20 Value at Origin s0 f 12 12 S 2f Parseval's Theorem n sn 2 f 12 12 S 2f 2 Discrete-time Fourier transform properties and relations.