2024 100606

B.Tech 6th Semester Examination, 2024

Time 03 Hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Q.1 Choose the correct answer of the following (any seven question only):

Q1.1

Which of the following is a continuous-time signal?

a)

Sinusoidal wave

b)

Impulse signal

c)

Unit step signal

d)

All of the above

Q1.2

What does DTFT stand for?

a)

Discrete-Time Fourier Transform

b)

Digital-Time Fourier Transform

c)

Dynamic-Time Fourier Transform

d)

Discrete Transfer Fourier Transform

Q1.3

The process of converting continuous-time signals into discrete-time signals is called?

a)

Quantization

b)

Sampling

c)

Lasing

d)

Reconstruction

Q1.4

What is the frequency domain representation of LTI systems called?

a)

Fourier Series

b)

Fourier Transform

c)

Laplace Transform

d)

Both i and ii

Q1.5

A system is causal if:

a)

Output depends on future inputs

b)

Output depends only on present and past inputs

c)

Output is independent of input

d)

None of the above

Q1.6

What is the result of convolving two impulse signals?

a)

Impulse signal

b)

Zero signal

c)

Step signal

d)

Constant signal

Q1.7

The sampling theorem states that to avoid aliasing, the sampling rate must be:

a)

Less than the Nyquist rate

b)

Equal to the Nyquist rate

c)

Greater than or equal to twice the maximum signal frequency

d)

Greater than the Nyquist rate

Q1.8

Which of the following is used to compute the convolution of two discrete signals?

a)

Fourier Transform

b)

Laplace Transform

c)

Z-transform

d)

Convolution sum

Q1.9

Which of the following represents the Nyquist rate?

a)

Twice the highest frequency

b)

Half the highest frequency

c)

Equal to the highest frequency

d)

None of the above

Q1.10

Which property of DFT leads to a reduction in computational complexity?

a)

Symmetry

b)

Linearity

c)

Circular convolution

d)

Time-shifting

Q.2 Solve both questions :

Q2.1

Explain the advantages of DSP over analog signal processing. Provide practical examples to support your explanation.

Q2.2

Discuss the stability and causality conditions of discrete-time systems. Provide examples of systems that are stable and causal.

Q.3 Solve both questions :

Q3.1

Explain the basic elements of a DSP system with a block diagram. How does it function in practical applications?

Q3.2

Compare the correlation and convolution of discrete-time signals with examples.

Q.4 Solve both questions :

Q4.1

Differentiate between continuous-time and discrete-time signals. Use diagrams to illustrate their key characteristics.

Q4.2

Explain the properties of the Discrete-Time Fourier Transform (DTFT) for LTI system with applications.

Q.5 Solve both questions :

Q5.1

Derive the formula for the Inverse Discrete-Time Fourier Transform with suitable examples.

Q5.2

Explain the process of sampling continuous-time signals and discuss the significance of the Nyquist rate in digital signal processing.

Q.6 Solve both questions :

Q6.1

Discuss the relationship between the time-domain and frequency-domain representations of signals using the Fourier transform.

Q6.2

Explain the reconstruction of signals from their samples using an ideal low-pass filter.

Q.7 Solve both questions :

Q7.1

Explain the difference between FIR and IIR filters. What are the advantages and disadvantages of each?

Q7.2

Discuss the properties of the Discrete Fourier Transform (DFT). Explain its significance.

Q.8 Solve both questions :

Q8.1

Derive the Fast Fourier Transform (FFT) algorithm and explain how it improves the computation of the DFT.

Q8.2

Determine the convolution for the two sequences $ x(n)=\{3,2,1,2\} $, $ h(n)=\{1,2,1,2\} $.

Q.9 Solve both questions :

Q9.1

Illustrate how the properties of linearity and time-invariance simplify the analysis of discrete-time systems with examples.

Q9.2

Explain the concept of periodicity in continuous-time and discrete-time signals. How do their periodicity conditions differ?

2024 V4 100606

B.Tech 6th Semester Examination, 2024

Time 03 Hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Q.1 Choose the correct answer of the following (any seven question only):

Q1.1

Which of the following is a continuous-time signal?

a)

Sinusoidal wave

b)

Impulse signal

c)

Unit step signal

d)

All of the above

Q1.2

What does DTFT stand for?

a)

Discrete-Time Fourier Transform

b)

Digital-Time Fourier Transform

c)

Dynamic-Time Fourier Transform

d)

Discrete Transfer Fourier Transform

Q1.3

The process of converting continuous-time signals into discrete-time signals is called?

a)

Quantization

b)

Sampling

c)

Lasing

d)

Reconstruction

Q1.4

What is the frequency domain representation of LTI systems called?

a)

Fourier Series

b)

Fourier Transform

c)

Laplace Transform

d)

Both i and ii

Q1.5

A system is causal if:

a)

Output depends on future inputs

b)

Output depends only on present and past inputs

c)

Output is independent of input

d)

None of the above

Q1.6

What is the result of convolving two impulse signals?

a)

Impulse signal

b)

Zero signal

c)

Step signal

d)

Constant signal

Q1.7

The sampling theorem states that to avoid aliasing, the sampling rate must be:

a)

Less than the Nyquist rate

b)

Equal to the Nyquist rate

c)

Greater than or equal to twice the maximum signal frequency

d)

Greater than the Nyquist rate

Q1.8

Which of the following is used to compute the convolution of two discrete signals?

a)

Fourier Transform

b)

Laplace Transform

c)

Z-transform

d)

Convolution sum

Q1.9

Which of the following represents the Nyquist rate?

a)

Twice the highest frequency

b)

Half the highest frequency

c)

Equal to the highest frequency

d)

None of the above

Q1.10

Which property of DFT leads to a reduction in computational complexity?

a)

Symmetry

b)

Linearity

c)

Circular convolution

d)

Time-shifting

Q.2 Solve both questions :

Q2.1

Explain the advantages of DSP over analog signal processing. Provide practical examples to support your explanation.

Q2.2

Discuss the stability and causality conditions of discrete-time systems. Provide examples of systems that are stable and causal.

Q.3 Solve both questions :

Q3.1

Explain the basic elements of a DSP system with a block diagram. How does it function in practical applications?

Q3.2

Compare the correlation and convolution of discrete-time signals with examples.

Q.4 Solve both questions :

Q4.1

Differentiate between continuous-time and discrete-time signals. Use diagrams to illustrate their key characteristics.

Q4.2

Explain the properties of the Discrete-Time Fourier Transform (DTFT) for LTI system with applications.

Q.5 Solve both questions :

Q5.1

Derive the formula for the Inverse Discrete-Time Fourier Transform with suitable examples.

Q5.2

Explain the process of sampling continuous-time signals and discuss the significance of the Nyquist rate in digital signal processing.

Q.6 Solve both questions :

Q6.1

Discuss the relationship between the time-domain and frequency-domain representations of signals using the Fourier transform.

Q6.2

Explain the reconstruction of signals from their samples using an ideal low-pass filter.

Q.7 Solve both questions :

Q7.1

Explain the difference between FIR and IIR filters. What are the advantages and disadvantages of each?

Q7.2

Discuss the properties of the Discrete Fourier Transform (DFT). Explain its significance.

Q.8 Solve both questions :

Q8.1

Derive the Fast Fourier Transform (FFT) algorithm and explain how it improves the computation of the DFT.

Q8.2

Determine the convolution for the two sequences $ x(n)=\{3,2,1,2\} $, $ h(n)=\{1,2,1,2\} $.

Q.9 Solve both questions :

Q9.1

Illustrate how the properties of linearity and time-invariance simplify the analysis of discrete-time systems with examples.

Q9.2

Explain the concept of periodicity in continuous-time and discrete-time signals. How do their periodicity conditions differ?

2022 100606

B.Tech Examination, 2022

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer the following questions (any seven) :

a)

List any two properties of discrete-time systems.

b)

Write the relationship between DFT and $Z$-transform.

c)

What is the condition on ROC for a system to be causal and stable?

d)

Write the differences between one-sided and two-sided $Z$-transforms.

e)

How is Chebyshev approximation different from Butterworth approximation in terms of frequency response of an LPF?

f)

If $X(k)$ is the $N$-point DFT of $x(n)$ , then what is the DFT of $W_N^{nl} x(n)$ ?

g)

What do you mean by transposed form structure?

h)

Define the term twiddle factor.

i)

What are the salient features of windowing technique?

j)

Define the term cross-correlation and write its significance.

Q2

Answer the following:

a)

Determine the solution of the difference equation $y(n) = \frac{5}{6}y(n-1) - \frac{1}{6}y(n-2) + x(n)$ when the forcing function is $x(n) = 2^n u(n)$ .

[7 Marks]

b)

A causal system is represented by $y(n) + 0.25y(n-1) = x(n) + 0.5x(n-1)$ Compute $H(z)$ and find the unit impulse response of the system in analytical form.

[7 Marks]

Q3

Answer the following:

a)

Explain in detail how a band-limited signal can be reconstructed from its samples in time and frequency domains without any loss of signal information.

[10 Marks]

b)

Determine the terms sampling theorem, Nyquist rate, Nyquist interval and aliasing.

[4 Marks]

Q4

Answer the following:

a)

Determine all possible signals of $x(n)$ associated with the following $Z$-transforms :

[12 Marks]

b)

Determine $Z$-transform and ROC of the finite-duration signal $x(n) = \{1, 0, 4, 5, 7, 0, 1\}$ (with the arrow pointing at the first 1)

[2 Marks]

Q5

Answer the following:

a)

State and prove time reversal property of DFT.

[3 Marks]

b)

Find the circular convolution of the two sequences $x_1(n) = \{1, 2, 3, 1\}$ and $x_2(n) = \{4, 3, 2, 2\}$ using concentric circles method. Verify the results using DFT-IDFT method.

[7 Marks]

c)

The 4-point DFT $x(n)$ (real sequence) is $X(k) = \{1, j, 1, -j\}$ . Find the DFT of the following sequences :

[4 Marks]

Q6

Answer the following:

a)

Realize the following system using direct form-I, direct form-II, cascade form and parallel form : $y(n) = 0.75y(n-1) - 0.125y(n-2) + 6x(n) + 7x(n-1) + x(n-2)$

[12 Marks]

b)

Realize the FIR filter given by $h(n) = (0.5)^n [u(n) - u(n-4)]$ using direct form-I.

[2 Marks]

Q7

Answer the following:

a)

Derive the expressions for order and cut-off frequency of a Butterworth filter.

[5 Marks]

b)

Determine the system function $H(z)$ of a Chebyshev filter type-I to meet the following specifications : \n - Passband ripple $\le 3$ dB \n - Stopband attenuation $\ge 20$ dB \n - Passband edge of $0.3\pi$ rad/sample \n - Stopband edge of $0.6\pi$ rad/sample \n Use bilinear transformation method and assume $T = 1$sec.

[9 Marks]

Q8

Answer the following:

a)

What are the effects of finite register length in the implementation of digital filters?

[4 Marks]

b)

Explain how the DFT and FFT are helpful in power spectral estimation.

[4 Marks]

c)

What is the need for multirate signal processing? Explain the process of interpolation and decimation with suitable examples.

[6 Marks]

Q9

Answer the following:

a)

Obtain the estimate of autocorrelation function and power spectral density for random signals.

[4 Marks]

b)

Explain the concept of Wiener filtering. Derive weight expression for Wiener filter and also obtain the expression for minimum mean square error.

[10 Marks]

2016 041710

B.Tech Examination, 2016

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer any seven questions :

a)

Find convolution of $x[n] = a^n u[n]$ and $G[n] = u[n]$ (use sum of sequence)

[2 Marks]

b)

If $x[n] = (6 - n)\{u[n] - u[n - 6]\}$ , sketch $y[n] = x(4 - n)$ .

[2 Marks]

c)

Find the correlation between the sequence $x(n) = u[n] - u[n - 6]$ and $G[n] = u(n - 2) - u(n - 5)$ .

[2 Marks]

d)

Define the linear phase filter.

[2 Marks]

e)

Find the frequency response of the parallel network shown in Fig.-1. The systems are Linear shift-invariant systems.

[2 Marks]

f)

Find the DTFT of the sequence $x_1[n] = a^n u[n]$ for $|a| < 1$ .

[2 Marks]

g)

Let $G[n]$ be the unit sample response of an linear shift invariant system. Find the frequency response when $G[n] = \delta[n] + 6\delta[n - 1] + 3\delta[n - 2]$ .

[2 Marks]

h)

Explain Nyquist Sampling theorem with proper mathematical expressions.

[2 Marks]

i)

If $X(Z)$ is $Z$ transform of $x[n]$ , then find the $Z$ transform of $nx[n]$ .

[2 Marks]

j)

Let $x[n]$ be the sequence $x[n] = 2\delta[n] + \delta[n - 1] + \delta[n - 3]$ then find four-point DFT of $x[n]$ .

[2 Marks]

[14 Marks]

Q2

a) Suppose that a sequence $x[n]$ has a $Z$ transform $X(z) = \frac{4 - \frac{7}{4}z^{-1} + \frac{1}{4}z^{-2}}{1 - \frac{3}{4}z^{-1} + \frac{1}{8}z^{-2}}$ with ROC $|z| > \frac{1}{2}$ find $x[n]$ using partial fraction expansion method. b) Discuss the advantages of DSP over analog processing.

a)

Suppose that a sequence $x[n]$ has a $Z$ transform $X(z) = \frac{4 - \frac{7}{4}z^{-1} + \frac{1}{4}z^{-2}}{1 - \frac{3}{4}z^{-1} + \frac{1}{8}z^{-2}}$ with ROC $|z| > \frac{1}{2}$ find $x[n]$ using partial fraction expansion method.

[7 Marks]

b)

Discuss the advantages of DSP over analog processing.

[7 Marks]

[14 Marks]

Q3

a) The $Z$-transform of a sequence $x[n]$ is $X(z) = \frac{z + 2z^{-2} + z^{-3}}{1 - 3z^{-4} + z^{-5}}$ if ROC include the unit circle. Then find the DTFT of $x[n]$ at $\omega = \pi$ . b) Evaluate the convolution of the two sequence $G[n] = (0.5)^n u[n]$ and $x[n] = 3^n u[-n]$ .

a)

The $Z$-transform of a sequence $x[n]$ is $X(z) = \frac{z + 2z^{-2} + z^{-3}}{1 - 3z^{-4} + z^{-5}}$ if ROC include the unit circle. Then find the DTFT of $x[n]$ at $\omega = \pi$ .

[7 Marks]

b)

Evaluate the convolution of the two sequence $G[n] = (0.5)^n u[n]$ and $x[n] = 3^n u[-n]$ .

[7 Marks]

[14 Marks]

Q4

a) A causal linear shift-invariant system is characterized by the difference equation $y[n] = \frac{1}{4}y[n - 1] + \frac{1}{8}y[n - 2] + x[n] - x[n - 1]$ . Find the system function $H(z)$ , and the unit sample response $G[n]$ . b) How may we compute the N-point DFT of two real-valued sequencer $x_1(n)$ and $x_2(n)$ , using one N-point DFT?

a)

A causal linear shift-invariant system is characterized by the difference equation $y[n] = \frac{1}{4}y[n - 1] + \frac{1}{8}y[n - 2] + x[n] - x[n - 1]$ . Find the system function $H(z)$ , and the unit sample response $G[n]$ .

[7 Marks]

b)

How may we compute the N-point DFT of two real-valued sequencer $x_1(n)$ and $x_2(n)$ , using one N-point DFT?

[7 Marks]

[14 Marks]

Q5

a) Consider two Sequence $x_1(n) = \cos(\frac{2\pi n}{n})$ and $x_2(n) = \sin(\frac{2\pi n}{N})$ . Find the N point circular convolution of $x_1(n)$ with $x_2(n)$ . (one DFT property) b) Design a Low pass buffer worth filler to meet the specifications $f_p = 6\text{ kHz}, f_s = 10\text{ kHz}, S_p = \delta s = 0.1$ .

a)

Consider two Sequence $x_1(n) = \cos(\frac{2\pi n}{n})$ and $x_2(n) = \sin(\frac{2\pi n}{N})$ . Find the N point circular convolution of $x_1(n)$ with $x_2(n)$ . (one DFT property)

[7 Marks]

b)

Design a Low pass buffer worth filler to meet the specifications $f_p = 6\text{ kHz}, f_s = 10\text{ kHz}, S_p = \delta s = 0.1$ .

[7 Marks]

[14 Marks]

Q6

Discuss with mathematical expression on decimation in time FFT algorithm also draw the eight point radix-2 butterfly signal flow diagram.

[14 Marks]

Q7

a) Consider the causal linear shift-invariant filter with system function $H(z) = \frac{(1 + 0.875z^{-1})}{(1 + 0.2z^{-1} + 0.9z^{-2})(1 - 0.7z^{-1})}$ . Draw a signal flow graph for the system using direct form II. b) Show that for bilinear transformation $S = \frac{2}{T} \frac{1 - z^{-1}}{1 + z^{-1}}$ where T is sampling duration.

a)

Consider the causal linear shift-invariant filter with system function $H(z) = \frac{(1 + 0.875z^{-1})}{(1 + 0.2z^{-1} + 0.9z^{-2})(1 - 0.7z^{-1})}$ . Draw a signal flow graph for the system using direct form II.

[7 Marks]

b)

Show that for bilinear transformation $S = \frac{2}{T} \frac{1 - z^{-1}}{1 + z^{-1}}$ where T is sampling duration.

[7 Marks]

[14 Marks]

Q8

a) Design a filter with $H_d(e^{j\omega}) = \begin{cases} e^{-j3\omega}, & \frac{-\pi}{4} \le \omega \le \frac{\pi}{4} \\ 0, & \frac{\pi}{4} \le |\omega| \le \pi \end{cases}$ using a Hamming window with $M=7$ b) Derive order formula for Chebyshev filter. Assume required parameters.

a)

Design a filter with $H_d(e^{j\omega}) = \begin{cases} e^{-j3\omega}, & \frac{-\pi}{4} \le \omega \le \frac{\pi}{4} \\ 0, & \frac{\pi}{4} \le |\omega| \le \pi \end{cases}$ using a Hamming window with $M=7$ .

[7 Marks]

b)

Derive order formula for Chebyshev filter. Assume required parameters.

[7 Marks]

[14 Marks]

Q9

a) Determine the IDFT of $x[u] = \{3, (2 + j), 1, (2 - j)\}$ . b) Consider the discrete time sequence $x[n] = \cos(\frac{n\pi}{8})$ . Find two different continuous time signal, that would produce this sequence when sampled at a frequency of $f_s = 10\text{ Hz}$ .

a)

Determine the IDFT of $x[u] = \{3, (2 + j), 1, (2 - j)\}$ .

[7 Marks]

b)

Consider the discrete time sequence $x[n] = \cos(\frac{n\pi}{8})$ . Find two different continuous time signal, that would produce this sequence when sampled at a frequency of $f_s = 10\text{ Hz}$ .

[7 Marks]

[14 Marks]

0 041710

B.Tech Examination, 0

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Choose the correct answer/Answer the following questions (any seven) :

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Write short notes on the following :

0 041710

B.Tech Examination, 0

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer any seven of the following questions :

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

What is DIT-FFT algorithm? How is it different from DIF-FFT algorithm? Compute the 8-point DFT of the sequence $x(n) = \\{1, -1, -1, -1, 1, 1, 1, -1\\}$ using DIT-FFT algorithm.

[14 Marks]

Q6

With the help of inverse Z-transform, determine all possible signals of $x(n)$ associated with the following :

[14 Marks]

Q7

Answer the following:

Q8

Answer the following:

Q9

Answer the following:

0 041710

B.Tech Examination, 0

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer any seven of the following :

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Write short notes on the following :

0 041810

B.Tech Examination, 0

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are EIGHT questions in this paper.
Attempt FIVE questions in all.
Questions No. 1 is compulsory.

Questions

Q1

Answer any seven question of the following :

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

0 104502

B.Tech Examination, 0

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer the following questions (any seven) :

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

What is the basic operation of radix-2 DITFFT algorithm? Compute the 8-point DFT of the sequence $x(n) = \\{1, 1, 1, 1, 1, 1, 1, 1\\}$ using this algorithm.

[14 Marks]

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Answer the following:

0 104502

B.Tech Examination, 0

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer any seven from the following :

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Write short notes on the following :