RAJ KUMAR GOEL INSTITUTE OF TECHNOLOGY FOR

WOMEN, GHAZIABAD 1 Sessional Test Subject code: EEC- 602

Branch: ECE Year: III Semester: VI

Time: 1 Hour Max Marks : 30

Subject: Digital Signal Processing

Attempt any five questions. All questions carry equal marks.

1. Show that the DFT of a sequence x(n) is purely imaginary & odd if the sequence x(n) is real & odd.

2. Find the 4 point DFT of the sequence x(n) = cos n/4.

3. Compute the convolution (both linear and circular) of the following sequences:

x(n) = { 1 , 1 , 0 , 1 , 1}

h(n) = { 1 , -2 , -3 , 4}

4. State and prove circular time & frequency shift of a sequence of DFT. Or

Prove the symmetry & periodicity property of twiddle factor.

5. Determine 2-point & 4-point DFT of a sequence

s(n) = u(n) u(n-2)

Sketch the magnitude of DFT in both the cases.

6. For the 8 sample sequence x(n) = { 1,2,3,5,5,3,2,1} , the first five DFT coefficients are { 22, -7.5355 j3.1213, 1 + j , -0.4645 j1.1213

, 0 }. Determine the remaining three DFT coefficients.