Topics

Frequency domain representation with example , Signal spectrum (amplitude & phase) ,Spectrum representation with example, Introduction to Fourier series , difference between Fourier series and Fourier transform ,Why Laplace and Z transform , Fourier series representation with example (sine)

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Intro ,First condition, Second condition , Third condition

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Intro to trigonometric Fourier series expression ,Mathematical representation of trigonometric Fourier series , Signal representation example ,shortcut conditions for Fourier series

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analyzing the signal and finding the value of a_0 and b_n,- Fourier series equation, calculating omega value , calculating the value of a_n ,substituting the value of a_n in the equation , simulation results / graphical explanation of signals

Topics

analyzing the signal ,Fourier series equation, calculating fundamental time period & x(t) value to calculate a_0 , calculating the value of a_n ,integration by using product rule/ integration by parts , calculating the b_n value , simulation results / graphical explanation of signals

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Introduction to relationship between complex exponential Fourier series and trigonometric Fourier series , Euler's Identity , relationship between coefficients

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Intro, Expression for complex exponential Fourier series coefficient ,Problem solution (rectangular signal)

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Intro to properties of Fourier Series, Linearity property, Conjugation property, Time reversal property, Time scaling property, Time shifting property, Frequency shifting property, Differentiation property, Integration in time property

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Intro to Fourier Transform - Fourier transform representation - Fourier Transform equation - Condition for existence of Fourier transform

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Intro - Linearity property - Time reversal property - Time scaling property - Time shifting property - Frequency shifting property - Convolution property - Differentiation in time - Differentiation in frequency

Topics

Intro - Problem 1 - Fourier transform of Exponential function - Problem 1- MATLAB simulation result - Problem 2 - Fourier transform of rectangular function - Problem 2 - MATLAB simulation result - Fourier transform of (del(t)) - Inverse Fourier transform of (del(omega)) - Inverse Fourier transform of (shifted del(omega) - Problem 3 - Fourier transform of cos(omega t) - Problem 4 - Fourier transform of sin(omega t)

Topics

Why Laplace Transform - what is integral transform - Representation of Laplace Transform - Equation of Laplace transform - Unilateral & bilateral Laplace transform - ROC - Region of Convergence - Inverse Laplace transform - Relationship between Fourier transform and Laplace transform

Topics

Intro - Existence of Laplace Transform - Finding ROC from an example - Definition of Region of Convergent - Zeros & Poles : from an example - Properties of ROC

Topics

Intro - Linearity property - Time reversal property - Time scaling property -Time shifting property - Frequency shifting property - Convolution in time - Multiplication in time - Differentiation in time - Integration in time

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Intro - Initial value theorem - Expression of differentiation property of unilateral Laplace transform - final value theorem

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Intro - Laplace transform of unit impulse signal - Laplace transform of unit step function - Shortcut for finding ROC - Laplace transform of an exponential function - Laplace transform of Cosine function - Table of Laplace transform of commonly used signals

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Intro - Question No1 : Laplace transform of a rectangular pulse - Question No2 : Laplace transform of exponential with ramp function - Question No3 : Previous year question (KTU sept 2020)

Topics

Introduction to Inverse Laplace transform - Eg No 1: Solution by considering ROC - Eg No 2 : Partial fraction method Step by step - Eg No 3 : Problem with multiple ROC - Eg No 4 : Function with higher order numerator , inverse Laplace transform of S

Question paper

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Fourth semester B.Tech examinations (S), SEPT 2020

Course Name: SIGNALS & SYSTEMS

Focused topics - Fourier Series, Fourier Transform and Laplace transform

Intro - Q4a) Determine the Complex exponential Fourier series of the wave shown - Q 4b) Obtain the Laplace transform of the following signals, indicating the region of convergence (ROC). - Q 5a) Find the Fourier Transform of the gaussian pulse - Q 5b) Explain the relationship between the Fourier transform & Laplace transform - Q 6b) Proof for differentiation property of unilateral Laplace transform

Question paper

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Fourth semester B.Tech examinations (S), SEPT 2020

Course Name: SIGNALS & SYSTEMS

Focused topics - Fourier Series, Fourier Transform and Laplace transform

Problem 4 b) Find the Fourier Transform of the following signal x(t). - 6 a) What is ROC of Laplace Transform? State any 5 properties of ROC. - 4 a) Derive the relation between Laplace transform and Continuous Time Fourier transform. - 4 b) Evaluate the Fourier Transform of x(t) = sgn(t). Plot magnitude and phase response. - 5 a) Determine the Fourier Series Representation for x(t)= 2sin(2πt-3) + sin(6πt).