Question

6. Explain via equations and/or words the following properties of Fourier Transforms: (3 points each) (a) Symmetry (b) Time Shifting (c) Frequency Shifting

Answer 1

symmetry cij even symmetry on is If X(t) signal then XCD = X(t) then kle can that even segnal has symmetry. say xct) M -2 2' lü) symmetry:- If x Et ) = -xct), then signal bes odd gormetoy pact) istih signal has (ii) Hidden symmetry :=1 *Ct) -4 (t+) then halfware symmetry axit) t ♡ Time shifting b the signal (shifting right side) delaging Adilancing & types I Time shifting is left the signal (shifting side) is Xcw) jie. xlt-to), then its fourrer If Fourier transform of act) then x (t) is deleated by to transform Jwt X (w) then its fourier pe. xcttt) If act) is advanced by to jut, X(w) transform PS e بابائے Foto of eat act) then fot lealt-te (t-t) (atiw I. atiw Ex: -

© Frequency shifting X(w) is -why shifting delaying is of 2 types advancing delayed If Inverse fourrer transform of Xcwrs XCD) by wo theire. X(w-wo), then its Pnverse fourier transform jwot xct) then its le Xcwtw.) If X(w) is advanced by w fourtër transform is x(t) (a+sw) = e atu eat act) is inverse ا به کج - Jwt e act) IET Ex?- jwot e IFT Latiw-ws] atj(w-wo)