Save as PDF
Opens your browser print dialog — select "Save as PDF" to download.
EC-402 (GS)
B.Tech. IV Semester
Examination, June 2024
Grading System (GS)
Signal and System
Note: i) Attempt any five questions:
ii) All questions carry equal marks.
iii) In case of any doubt or dispute the English version question should be treated as final.
a) Distinguish between the following:
i) Continuous time signal and discrete time signal
ii) Unit step and Unit Ramp functions
iii) Periodic and Aperiodic Signals
iv) Deterministic and Random Signals
i) सतत समय संकेत और असतत समय संकेत
ii) इकाई चरण और इकाई रैंप फंक्शन
iii) आवधिक और अनावर्ती संकेत
iv) नियतात्मक और यादृच्छिक संकेत
b) Determine whether the following function is periodic or not. If so find the period.
\(x(t) = 3\sin 200\pi t + 4\cos 100t\)
\(x(t) = 3\sin 200\pi t + 4\cos 100t\)
a) Check linearity and causality of the following systems:
i) \(d^3y(t) \over dt^3 + 7{d^2y(t) \over dt^2} + 9{dy(t) \over dt} + y(t) = x^2(t)\)
ii) \(y(n) = x(n)x(n-2)\)
b) What is LTI system? How discrete time LTI system differs from continuous time LTI system. What is the importance of impulse response to LTI System? Explain in detail.
a) Calculate the output of the LTI system whose impulse response and input are given by
\(h(t) = e^{-at}u(t)\) and \(x(t) = e^{at}u(t)\)
\(h(t) = e^{-at}u(t)\) और \(x(t) = e^{at}u(t)\)
b) ALTI System is described by the following differential equation. Find out its impulse response by assuming all initial condition to be zero.
\({d^3y \over dt^3} + 4{d^2y \over dt^2} + 2{dy \over dt} + y(t) = 3x(t)\)
\({d^3y \over dt^3} + 4{d^2y \over dt^2} + 2{dy \over dt} + y(t) = 3x(t)\)
a) State and prove the time shifting, differentiation and integration properties of Z transform.
b) Find the inverse Z-transform of X(z) = 1/(1 + z) with ROC |z| < 1.
a) Prove that the sequence \(a^n u(n)\) and \(x(n) = -a^n u(-n-1)\) have the same X(z) and differ only in ROC. Also plot their ROC.
b) Find the Fourier transform of \(e^{-3t} \sin(\omega_0 t) u(t)\).
a) Find the Fourier series of the following discrete-time signal.
\(x(n) = 1 + \sin\left(\frac{2\pi}{5}n\right) + 3\cos\left(\frac{2\pi}{5}n\right) + \cos\left(\frac{4\pi}{5}n\right)\)
\(x(n) = 1 + \sin\left(\frac{2\pi}{5}n\right) + 3\cos\left(\frac{2\pi}{5}n\right) + \cos\left(\frac{4\pi}{5}n\right)\)
b) List and explain various properties of Fourier transform.
a) State and prove sampling theorem for band-limited signals.
b) Describe state-transition matrix and its role.
Write a short note on any two :
a) State space analysis
b) Convergence of discrete time Fourier Transform
c) Unilateral Z-Transform
d) Convolution
अ) स्टेट स्पेस विश्लेषण
ब) असतत समय फूरियर ट्रांसफॉर्म का अभिसरण
स) एकतरफा Z-ट्रांसफॉर्म
द) कनवोल्यूशन
******