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JNTU B.Tech IV Year DIGITAL SIGNAL PROCESSING Previous Question Paper (July/August - 2022 - R18)

B.Tech | IV Year | I Semester | R18 | July/August - 2022

Answer PaperPaper Code: 157BGMaximum Marks: 75Time: 3 Hours

Answer any five questions. All questions carry equal marks.

Main

115 marks

Define stability and causality. State the conditions for discrete systems for stable and causal.

8 marks

Answer

A system is stable if every bounded input produces a bounded output (BIBO stability). A system is causal if the output at any time instant depends only on the present and past inputs, and not on future inputs.

The conditions for a discrete-time Linear Time-Invariant (LTI) system are:

Stability: The impulse response h(n) must be absolutely summable, expressed as:
Σ |h(n)| < ∞ for all n from -∞ to +∞
Causality: The impulse response h(n) must be zero for all negative time indices:
h(n) = 0 for n < 0

Determine the response of the system with impulse response

h(n)=a^n u(n)

to the input signal.

7 marks

Answer

The response y(n) of an LTI system is the convolution of the input x(n) and the impulse response h(n) = aⁿu(n). The convolution sum is defined as:

y(n) = Σ x(k)h(n-k) = Σ x(k)a^n-ku(n-k)

Since h(n-k) is non-zero only when n-k ≥ 0 (i.e., k ≤ n), the summation limits change to:

y(n) = aⁿ Σ x(k)a^-k for k = -∞ to n

If the input x(n) = u(n) (unit step), the response becomes:

y(n) = aⁿ Σ a^-k for k = 0 to n

Using the geometric series formula Σ r^k = (1 - rⁿ⁺¹)/(1 - r), where r = a^-1:

y(n) = aⁿ [ (1 - (a^-1)ⁿ⁺¹) / (1 - a^-1) ] u(n) = [ (aⁿ⁺¹ - 1) / (a - 1) ] u(n)

215 marks

For linear constant coefficient difference equation calculate the frequency response

y(n)=0.6 y(n-1)-0.1y(n-2)+x(n)

to the input signal

x(n)=δ(n)

8 marks

Answer

Derive the expressions for up sampling and down sampling.

7 marks

Answer

315 marks

Derive the relation between DFS and DTFT.

7 marks

Answer

Compute the circular convolution of the sequences

x(n)=[1, 2, 3, 1]

;

h(n)=[4, 3, 2, 2]

; using time domain formula.

8 marks

Answer

415 marks

Compute the eight point DFT of the sequence

x(n)={0.5, 0.5, 0.5, 0.5, 0, 0, 0, 0}

using DIT-FFT algorithm.

9 marks

Answer

Compare overlap add and overlap save method.

6 marks

Answer

Using the design formulas find the order and system function

H(z)

of digital Butterworth filter for IIR LPF with passband ripple ≤ 0.5 dB, passband edge = 1.2 kHz, stopband attenuation ≥ 0 dB, stop band edge 2 kHz, sampling rate 8 kHz.

15 marks

Answer

615 marks

Explain the Bilinear transformation method for designing IIR filter using design formulas.

8 marks

Answer

List the frequency transformations relations for analog filters from low pass filter to high pass, band pass and band stop filter.

7 marks

Answer

715 marks

Compare the characteristics of IIR and FIR filters.

5 marks

Answer

Design an FIR linear phase digital filter with order 7, approximating the ideal frequency response

H(ω)=1

for

|ω|≤π/6

; and 0 for

π/6≤|ω|≤π

10 marks

Answer

815 marks

Realize the system defined by the difference equation given by

y(n) = 2.5y(n-1)-y(n-2)+x(n)-5x(n-1)+6x(n-2)

using direct form I and direct form II.

8 marks

Answer

Compute convolution of two signals {1, 2, 3, 4} and {4, 3, 2, 1} using Z-transform.

7 marks

JNTU B.Tech IV Year DIGITAL SIGNAL PROCESSING Previous Question Paper (July/August - 2022 - R18)

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