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JNTU B.Tech III DIGITAL SIGNAL PROCESSING Previous Question Paper (April - 2018 - R15)

B.Tech | III | III-II | R15 | April - 2018

Answer PaperPaper Code: 126VKMaximum Marks: 75Time: 3 hours

Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.

Part A

25 Marks

Show that

δ(n) = u(n) – u(n-1)

2 marks

Answer

The unit step function is defined as u(n) = 1 for n ≥ 0 and u(n) = 0 for n < 0. Similarly, the shifted unit step function is u(n-1) = 1 for n ≥ 1 and u(n-1) = 0 for n < 1. Subtracting these two functions yields:

u(n) - u(n-1) = 1 - 0 = 1 for n = 0

u(n) - u(n-1) = 1 - 1 = 0 for n ≥ 1

u(n) - u(n-1) = 0 - 0 = 0 for n < 0

Since the result is 1 only at n = 0 and 0 elsewhere, it satisfies the definition of the unit impulse function δ(n).

Find the Z-transform

f(n) = nu(n)

3 marks

Answer

The Z-transform of a discrete-time signal f(n) is defined as F(z) = Σ f(n)z^-n for n from -∞ to ∞. Given f(n) = nu(n), the signal is non-zero only for n ≥ 0, where u(n) is the unit step function.

Substituting the signal into the definition:

F(z) = Σ n z^-n (for n=0 to ∞)

Using the standard power series identity Σ n xⁿ = x / (1-x)² for |x| < 1, let x = z^-1:

F(z) = z^-1 / (1 - z^-1)²

Multiplying the numerator and denominator by z²:

F(z) = z / (z - 1)²

The Region of Convergence (ROC) for this transform is |z| > 1.

State and prove the any three properties of DFT.

2 marks

Answer

What is the basic operation of DIF algorithm?

3 marks

Answer

What are the properties of Butterworth Low pass filter?

2 marks

Answer

Discuss the stability of the impulse invariant mapping technique

3 marks

Answer

Explain the effects of truncating an infinite Fourier series into a finite series.

2 marks

Answer

What is the condition for the impulse response of FIR filter to satisfy for constant group and phase delay and for constant group delay?

3 marks

Answer

What is the need for Multirate Digital Signal Processing

2 marks

Answer

What do you mean by quantization step size?

3 marks

Answer

Part B

50 Marks

210 marks

An LTI system is characterized by an impulse response

h(n) = (3/4)^n u(n)

. Find the step response of the system. Also, evaluate the output of the system at n=±5.

5 marks

Answer

Consider a discrete-time system characterized by the following input-output relationship

y(n) = x(n-2) - 2x(n-17)

. Determine whether the system is memoryless, time-Invariant, linear, causal and stable.

5 marks

Answer

310 marks

Given the difference equation

y(n) + b^2 y(n-2) = 0

for

n ≥ 0

and

b < 1

. With initial conditions

y(-1) = 0 and y(-2) = -1

, Show that

y(n) = b^n cos(nπ/2)

5 marks

Answer

Find the Z-transform of the sequence f(n) defined below:

5 marks

Answer

410 marks

Find the IDFT of the sequence X(K) given below

X(K) = {1, 0, 0, j, 0, -j, 0, 0}

5 marks

Answer

Obtain the 10 point DFT of the sequence

x(n) = δ(n) + 2δ(n-5)

5 marks

Answer

510 marks

Find the IDFT of the sequence

X(K) = {20, -5.828-j2.414, 0, -0.712-j0.414, 0, -0.172+j0.414, 0, -5.828+j2.414}

using DIT-FFT algorithm.

5 marks

Answer

Using FFT and IFFT, determine the output of system if input

x(n)={2, 2, 4}

and impulse response

h(n) = {1, 1}

5 marks

Answer

610 marks

Design a digital low pass filter using Chebyshev filter that meets the following Specifications: Passband magnitude characteristics that is constant to within 1dB for recurrences below

ω = 0.2π

and stopband attenuation of atleast 15dB for frequencies between

ω = 0.3π and π

. Use bilinear transformation.

5 marks

Answer

An analog filter has the following system function. Convert this filter into a digital filter by using the impulse invariant technique:

H(s) = 1/((s+0.1)^2 + 9)

5 marks

Answer

710 marks

Using a bilinear transformation, design a Butterworth filter which satisfies the following conditions:

0.8 ≤ |H(e^{jω})| ≤ 1 for 0 ≤ ω ≤ 0.2π

and

|H(e^{jω})| ≤ 0.2 for 0.6π ≤ ω ≤ π

5 marks

Answer

Determine H(z) using impulse invariance method for the following system function:

Ha(s) = 1/((s+0.5)(s^2 + 0.5s + 2))

5 marks

Answer

810 marks

The desired frequency response of a low pass filter is given. Find

H(e^{jω})

for M=7 using a rectangular window.

5 marks

Answer

Explain the type II frequency sampling method of designing an FIR digital filter.

5 marks

Answer

910 marks

Design a band pass filter which approximates the ideal filter with cutoff-frequencies at 0.2rad/sec and 0.3rad/sec. The filter order is M=7. Use the Hanning window function.

5 marks

Answer

Design an ideal band pass filter with a given frequency response.

5 marks

Answer

1010 marks

Explain the interpolation process for an integer factor I with an example.

5 marks

Answer

Given the limit cycle behavior

y(n) = 0.7y(n-2) + 0.52y(n-1) + x(n)

. Find the dead band of the above two systems.

5 marks

Answer

1110 marks

The signal x(n) is defined by

g(n) = A^n

for

n > 0

, 0 otherwise. i) Obtain the decimated signal with a factor of 3. ii) Obtain the interpolated signal with a factor of 3.

5 marks

Answer

Given the system

y(n) = 1/2 y(n-1) + x(n)

. i) Calculate the response to the input

x(n) = (1/4)^n u(n)

assuming infinite precision arithmetic. ii) Calculate the response y(n),

0 ≤ n ≤ 5

to the same input assuming finite precision with five bits, one sign bit plus four fractional bits. The quantization is performed by truncation. Discuss the results.

5 marks

JNTU B.Tech III DIGITAL SIGNAL PROCESSING Previous Question Paper (April - 2018 - R15)

Part A

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Part B

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