Exam 2 Solution Spring 209

The only nonzero samples of xn over the range 0 to 7

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n, i.e. xŒ0; xŒ1; : : : ; xŒ7. Show and motivate your calculations. The only nonzero samples of xŒn over the range 0 to 7 are xŒ2 D 1 and xŒ6 D DFT is therefore XŒk D 7 X nD0 De D xŒnW8k n j . 2 8 /2k D e 2j j.  /k .e 2 2j 7 X xŒne j . 2 /k n 8 nD0 j . 2 /6k 8 e j .  /k 2 De /D j .  /k 2  e j. 2 /k 2j sin.k=2/: Therefore XŒ0 D XŒ4 D 0 XŒ1 D XŒ5 D 2j D 2e j =2 XŒ2 D XŒ6 D 0 XŒ3 D XŒ7 D 2j D 2e j=2 : Magnitude and phase plots are as follows: 2 |X[k]| 1.5 1 0.5 0 0 1 2 3 4 5 6 7 4 5 6 7 k 2 ∠(X[k]) 1 0 −1 −2 0 1 2 3 k 1. The 3. (5 marks) Conside...
View Full Document

Ask a homework question - tutors are online