Questions

 

A. Fourier Transform properties

 

(a) If x ( t ) is real and even, show that its Fourier transform is real for all ω (i.e., its imaginary part is  identically 0).

 

(b) If x ( t ) is real and odd, show that its Fourier transform is imaginary for all ω (i.e., its real part is identically 0)

 

 

 

B.Discrete-time Fourier Transform (DTFT)

 

B. Compute the DTFT of the following signals:

 

(a) a [ n ] = δ [ n − 2] + δ [ n + 2]

 

(b) b [ n ] = u [ n ] − u [ n − 4]

 

(c) c [ n ] = ( sin (( π/ 4) n )/ πn ) ^2

 

 

 

Attachments: 

  1. Fourier Transform properties

(a) If x ( t ) is real and even, show that its Fourier transform is real for all ω (i.e., its imaginary part is  identically 0).

(b) If x ( t ) is real and odd, show that its Fourier transform is imaginary for all ω (i.e., its real part is identically 0)

 

B.Discrete-time Fourier Transform (DTFT)

  1. Compute the DTFT of the following signals:

(a) a [ n ] = δ [ n − 2] + δ [ n + 2]

(b) b [ n ] = u [ n ] − u [ n − 4]

(c) c [ n ] = ( sin (( π/ 4) n )/ πn ) ^2