(SEM V) THEORY EXAMINATION 2022-23 DIGITAL SIGNAL PROCESSING

Course: B.Tech (Semester V)                                                           Subject Code: KEC-503

Subject Name: Digital Signal Processing                                       Time: 3 Hours

Total Marks: 100

Note: Attempt all sections. Assume data wherever required. 

Section A – Short Answer Questions (2 × 10 = 20 Marks)

Answer all briefly:

Explain basic elements of a digital signal system.

Difference between recursive and non-recursive systems.

Calculate DFT of sequence x(n)={1,2,1,3}x(n) = \{1, 2, 1, 3\}x(n)={1,2,1,3}.

Define Twiddle Factor and its properties.

Difference between Circular Convolution and Linear Convolution.

Explain Frequency Warping.

Describe Gibbs Phenomenon with diagram.

Write the expression for Hanning Window.

Explain Decimation with example.

Find the output of sequence [1 2 3] after upsampling by factor N=3N = 3N=3. 

Section B – Descriptive Questions (10 × 3 = 30 Marks)

Attempt any three:

Determine DF-I and DF-II realization for the IIR transfer function:
H(z)=0.28z2+0.319z+0.040.5z3+0.3z2+0.17z−0.2H(z) = \frac{0.28z^2 + 0.319z + 0.04}{0.5z^3 + 0.3z^2 + 0.17z - 0.2}H(z)=0.5z3+0.3z2+0.17z−0.20.28z2+0.319z+0.04​.

Explain Impulse Invariance Method for IIR filter design and mapping of poles from analog to digital domain.

Discuss finite word length effects in digital filters — coefficient quantization and truncation errors.

Derive and draw the flow graph for DIT-FFT algorithm for N=8N = 8N=8.

Discuss QMF and sub-band coding of speech signals. 

Section C – Long Answer Questions (10 × 5 = 50 Marks)

Q3

(a) Obtain Direct Form and Cascade Form realization for
H(z)=(1−14z−1+38z−2)(1−18z−1−12z−2)H(z) = (1 - \frac{1}{4}z^{-1} + \frac{3}{8}z^{-2})(1 - \frac{1}{8}z^{-1} - \frac{1}{2}z^{-2})H(z)=(1−41​z−1+83​z−2)(1−81​z−1−21​z−2).
or
(b) Explain DSP Technologies and compare IIR and FIR filters.

Q4

(a) Using Bilinear Transformation, design a Butterworth Filter satisfying:
0.8≤∣H(ejω)∣≤1,0≤ω≤0.2π0.8 \le |H(e^{j\omega})| \le 1, 0 \le \omega \le 0.2\pi0.8≤∣H(ejω)∣≤1,0≤ω≤0.2π
and ∣H(ejω)∣≤0.2,0.6π≤ω≤π|H(e^{j\omega})| \le 0.2, 0.6\pi \le \omega \le \pi∣H(ejω)∣≤0.2,0.6π≤ω≤π.
or
(b) Obtain System Function of a digital filter resonant at ωr=π/2\omega_r = \pi/2ωr​=π/2 from
H(s)=s+0.1(s+0.1)2+16H(s) = \frac{s + 0.1}{(s + 0.1)^2 + 16}H(s)=(s+0.1)2+16s+0.1​.

Q5

(a) Design a Symmetric FIR Low-Pass Filter of length 7 with cutoff ωc=1\omega_c = 1ωc​=1 rad/sample using Rectangular Window.
or
(b) Explain Limit Cycle Oscillations and Dead Band Effect with examples.

Q6

(a) Find DFT of x(n)={1,1,2,2,3,3}x(n) = \{1, 1, 2, 2, 3, 3\}x(n)={1,1,2,2,3,3} and determine amplitude and phase spectrum.
or
(b) Compute DFT of x(n)={1,−1,−1,−1,1,1,1,−1}x(n) = \{1, -1, -1, -1, 1, 1, 1, -1\}x(n)={1,−1,−1,−1,1,1,1,−1} using DIF-FFT Algorithm.

Q7

(a) Compute Circular Convolution using graphical method for
x(n)=[1,2,3,4]x(n) = [1, 2, 3, 4]x(n)=[1,2,3,4], h(n)=[4,3,2,1]h(n) = [4, 3, 2, 1]h(n)=[4,3,2,1].
or
(b) Explain Multirate Signal Processing and its advantages.