Regd.No.
R23
KALLAM HARANADHAREDDY INSTITUTE OF TECHNOLOGY (AUTONOMOUS)
Subject Code: R23XXXX
II B. Tech I Semester (R23) Regular Examinations, November- 2024
SIGNALS AND SYSTEMS
ECE
Time: 3 hours Max. Marks: 70
Answer Question No.1 is compulsory (10X2=20M)
Answer ONE question from each unit (5×10 = 50M)
Q.No Questions Marks
1 A How to represent discrete time signals? 2M
B Define causal and non-causal systems. 2M
C What are three important classes of Fourier series methods available? 2M
D What is Fourier transform? 2M
E Define the impulse response of a system. 2M
F What is a filter? 2M
G Differentiate ESD and PSD? 2M
H What is Nyquist rate and Nyquist interval? 2M
I What is the Region of Convergence (ROC)? 2M
J State the linear Property of Z-transform 2M
2 A i Write about elementary Continuous time Signals in Detail. 5M
ii Examine whether the following signal is periodic or not? If periodic determine 5M
the fundamental period. 𝑥(𝑡) = 3 𝑠𝑖𝑛 200𝜋𝑡 + 4 𝑐𝑜𝑠100𝜋𝑡
Or
B i Explain the Analogy between vectors and signals. 5M
ii Prove that sinnωot and cosmωot are orthogonal to each other for all integer 5M
values of m, n.
5M
3 A i State Dirichlet’s conditions of Fourier series. 5M
ii State and prove any three properties of Fourier Series. 5M
Or
B i State and prove any four properties of Fourier Transform 5M
ii Find the Fourier transform of x(t)= te -at u(t) 5M
4 A i What is an LTI system? Derive an expression for the transfer function of an 5M
LTI system.
ii 5M
Explain distortion less transmission through a system.
Or
B i 1 5M
Consider a causal LTI system with frequency response 𝐻(𝜔 ) = . for a
4+𝑗𝜔
particular input x(t) produces the output 𝑦(𝑡 ) = 𝑒 −2𝑡 𝑢(𝑡) − 𝑒 −4𝑡 𝑢(𝑡 ).Find
the input x(t).
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ii A system produces an output of 𝑦 (𝑡 ) = 𝑒 −𝑡 𝑢(𝑡) for an input of 𝑥(𝑡) = 5M
𝑒 −2𝑡 𝑢(𝑡) determine the impulse response and frequency response of the
system
5 A i Explain autocorrelation function and list it properties. 5M
ii Find convolution of given signals using Fourier transform. 5M
𝑥1 (𝑡) = 𝑒 −𝑡 𝑢 (𝑡) , 𝑥2 (𝑡) = 𝑒 −𝑡 𝑢(𝑡 )
Or
B i
Define sampling theorem and explain Nyquist rate of sampling. 5M
ii Determine the Nyquist sampling rate and Nyquist sampling interval for the
5M
below signal.
x(t) =1+ cos2000πt+Sin4000πt
6 A i Find the Laplace Transform of following signal and its ROC. 5M
𝑥 (𝑡 ) = 𝑒 −𝑡 𝑢 (𝑡) + 𝑒 −4𝑡 𝑢(𝑡)
ii 5M
Find the inverse Laplace transform of
𝑠
𝑋(𝑠) =
(s + 1)2 + 1
Or
B i Using final value theorem find 𝑥 (∞) if
𝑧+2 5M
𝑋 (𝑍 ) =
4(𝑧 − 1)(𝑧 + 0.7)
ii
Find the Inverse Z transform of
2𝑧 3 −5𝑧 2+𝑧+4 5M
𝑋 (𝑧 ) = (z−1)(z−2)
, |𝑧 | <1
****
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