ece 2107 pyq

Here is the brutal, exhaustive, and rigorously categorized PYQ breakdown. If a question appeared in multiple years with the exact same wording, they are grouped. If even a single word, punctuation mark, or numerical value differed, they are kept separate to expose the examiner’s pattern of tweaking variables.

Table 1: Signals & Systems Fundamentals (Definitions, Classifications, Stability)

Subtopic	Exact Question [mark]	Year(s) of Appearance
Basic Definitions	What is signal & system?	2025
	What are signal and system? What are the importance of these in communication engineering?	2024
	What are meant by signal and system?	2023
	Define: (i) Unit step function, (ii) Unit impulse function, (iii) Ramp function, and (iv) Signum function	2022
	Define signal. Classify signals based on major criterias.	2021
	Define: (i) Signal, (ii) System, (iii) Shanon-Nyquist Sampling Theorem.	2020
	What are the major classifications of signals? Explain the operations performed on the independent variables in the processing of discrete signals.	2019
	What is signal? What are the major classifications of signal? Explain the operations performed on the independent variables in the processing of discrete signals mathematically & graphically. [11/12]	2018, 2015
	What is signal? Explain the operations performed on the independent variables in the processing of discrete signals.	2017
	What is signal? What are the major classifications of signals?	2016
	Define system. What are properties of a system?	2025
	Define system. What are the properties of a system? [06/07]	2024, 2023, 2019, 2018
	What is system? What are the properties of a system?	2016
	Define system. Distinguish between: (i) Causal and Non-causal system. (ii) FIR & IIR System	2015
	Define system. Distinguish between: i) Linear and Non-linear system. ii) Recursive and Non-recursive system.	2017
	Write short notes on : (i) invertible system, (ii) memoryless system, (iii) recursive system	2016
	Write short notes on (i) Memoryless system and (ii) Recursive System.	2024
	Discuss about the characterization of discrete-time systems.	2023
	Classify discrete time signals.	2020
	Distinguish between (i) deterministic and nondeterministic signals; (ii) even and odd signals.	2018
Energy & Power	Determine whether $x(n)=\{\begin{array}{l}\sin (\pi n);n\ge 00,otherwise\end{array}$ is energy or power signal and also find its corresponding energy or power.	2025
	Determine whether $x(n)=\{\begin{array}{l}\cos (\pi n);n\ge 00;Otherwise\end{array}$ is energy or power signal and also find its corresponding energy or power.	2023
	Determine whether $x(n)=\{\begin{array}{l}\cos (\pi n);n\ge 00;otherwise\end{array}$ is energy or power signal and also find its corresponding energy or power.	2019
	Determine whether $x(n)=\{\begin{array}{l}\cos (\pi n);-4\le n\le 40;otherwise\end{array}$ is energy or power signal and also find its energy/power.	2018
	Determine whether $x(n)=\{\begin{array}{l}n;0\le n<510-n;5\le n\le 100;otherwise\end{array}$ is energy or power signal and also find its energy or power.	2017
	Determine the power and energy of the continuous time signal $x(t)=u(t)=\{\begin{array}{l}1,t\ge 00,t<0\end{array}$	2022
	Consider a signal $x(t)=5\cos (\pi t)+\sin (5\pi t),-\infty <t<\infty$. Determine if it is an energy signal or a power signal and also find its energy/power.	2016
	Determine whether the signal, $x(t)=\sin \sqrt{2}\pi t+\sin 15\pi t$ is periodic or not, then find its fundamental period. Also, compute the energy of that signal.	2015
Even & Odd Signals	If $x_e(t)$ and $x_o(t)$ are even and odd parts of x(t), show that ${\int }_{-\infty }^{\infty }{x}^2(t)dt={\int }_{-\infty }^{\infty }{x}_e^2(t)dt+{\int }_{-\infty }^{\infty }{x}_o^2(t)dt$ [07/10]	2024, 2023, 2021
	Find the odd and even components for each of the following signals: (i) $x(t)=u(t)$; (ii) $x(t)=e^{-\alpha t}u(t)$;	2020
	Find the Even and Odd components of the given signal: $x(t)=\cos (20\pi t-5\pi )$ and also, sketch the signal.	2018, 2015
	Determine whether the signal $x(t)=\sin \sqrt{2}\pi t+\sin 15\pi t$ is periodic or not. Then find its fundamental period. Also, determine the even and odd components of the signal.	2019
Periodicity	For the following signals, determine whether it is periodic or aperiodic. If periodic, find period $x(t)=2\cos (4\pi t)+3\sin (3\pi t)$	2025
	Determine whether the signal $x(t)=\sin 20\pi t+\sin 5\pi t$ is periodic or not. If it is periodic, then find the fundamental period.	2017
	Consider a signal: $x(t)=10\sin \sqrt{5}\pi t$, (i) Is it periodic? If it is, find its fundamental period. (ii) Is it even or odd?	2016
Signal Sketching	Sketch the following signals: (i) $x(t)=-4r(3t-1)$; (ii) $x(t)=\pi (2t+5)$	2024
	Sketch the following signals: (i) $x(t)=4r(3t-1)$, (ii) $x(t)=\pi (2t+5)$.	2019
	Sketch the following signals: i) $x(t)=2r(0.5t+0.25)$ and ii) $x(t)=5(2t+1)$	2017
	Sketch the following signals: (i) $(t)=\prod (2t+3)$, (ii) $x(t)=\cos (20\pi t-5\pi )$.	2016
	Sketch the signals: i) $u(t-5)-u(t-7)$, ii) $t^2[u(t-1)-u(t-2)]$, iii)$sin(50t-\pi /4)$.	2021
	Sketch the following signal: $x(t)=r(-0.5t+2)$	2015
	Write down the corresponding equation for the given signal in figure 1(e). i) Represent through addition of unit step functions. ii) Represent through multiplication of unit step functions.	2015
System Properties (LTI, Causal, Linear, Time-Variant)	State whether the signals are causal, anticausal or noncausal: $x(t)=e^{-2t}u(t)$	2025
	State whether the following signals are causal, anticausal or noncausal. (i) $x(t)=e^{-2t}u(t)$; (ii) $x(t)=tu(t)$	2020
	Determine if the following continuous-time system is time invariant or time variant. $y(t)=3x(-t)+2x(t)$	2025
	Determine if the following continuous-time system is time invariant or time variant: $y(t)=3x(-t)+2x(t)$	2022
	A discrete-time system is represented by the following difference equation in which x(n) is input and y(n) is output. $y(n)=3y(n-1)-n^{2}x(n)+4x(n-1)-2x(n+1)$. Determine whether the system is (i) Time invariant, (ii) Linear, and (iii) Causal.	2024
	The discrete-time system is represented by the following difference equation in which x(n) is input and y(n) is output: $y(n)=3y(n-1)-n^{2}x(n)+4x(n-1)-2x(n+1)$. Determine whether the system is (i) Time invariant (ii) Linear (iii) Causal	2019
	Determine if the following continuous-time system is linear or nonlinear: $\frac{dy}{dt}+3y(t)=x(t)\frac{dx(t)}{dt}$	2022
	Determine the following system is linear or nonlinear. $\frac{dy(t)}{dt}+3y(t)=x^2(t)$	2020
	What is LTI system? Determine whether the system described by differential equation $\frac{dy(t)}{dt}+3y(t)+4=x(t)$ is linear.	2016
	The discrete-time system is represented by the following difference equation in which x(n) is input and y(n) is output: $y(n)=4y^2(n-1)-nx(n)+3x(n-1)-2x(n+1)$. Determine whether it is, (i) time invariant; (ii) causal; (iii) linear; and (iv) FIR/IIR system.	2018
	Determine whether the discrete time system represented by the difference equation: $y(n)=x(n+1)-3x(n)+x(n-1);n\ge 0$. i) Time invariant, ii) Linear, and iii) Causal	2017
	The discrete-time system is represented by the following difference equation in which x(n) is input & y(n) is output: $y(n)=3y^2(n-1)-nx(n)+4x(n-1)-2x(n+1)$. Determine whether it is - i) Time invariant, ii) Linear, iii) Causal.	2015
System Stability (BIBO)	Check the BIBO stability of the following system: $y(n)=ax(n+1)+bx(n-1)$.	2020
	Check the BIBO stability of the following systems: $y(n)=ax(n+1)+bx(n-1)$.	2019
	Briefly discuss the process of determining system stability.	2021
	Deduce the necessary and sufficient condition of BIBO stability of an LTI system. Also check the BIBO stability of the digital system: $y(n)=e^{-x(n)}$	2017
	What do you mean by system stability? What is necessary & sufficient condition for the stability of a DSP system? Also determine H(z) and its poles & zeros if $y(n)+\frac{3}{4}y(n-1)+\frac{1}{8}y(n-2)=x(n)+x(n-1)$	2016
	Deduce the sufficient & necessary condition for Bounded Input Bounded Output (BIBO) stability of an LTI system. Also check the BIBO stability for the digital filter: $y(n)=x(n)+e^{n}y(n-1)$.	2015

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Table 2: Time-Domain System Analysis (Convolution, Difference/Differential Equations)

Subtopic	Exact Question [mark]	Year(s) of Appearance
Convolution Properties & Proofs	If $y(t)=x(t)\ast h(t)$ then show that, $y(2t)=2x(2t)\ast h(2t)$	2025
	If $y(t)=x(t)\ast h(t)$, then show that $y(2t)=2x(2t)\ast h(2t)$.	2022
	Show that the output response of an LTI system is the convolution sum of the input signal and impulse response.	2023
	Show that the output response of a LTI system is the convolution sum of the input signal and impulse response.	2017
	Show that the output response of an LTI system is the convolution sum of the input signal & impulse response of the system.	2015
	Derive the expression of convolution with delay input and delayed impulse response.	2021
Calculating Convolution	Find the convolution of the sequences $x[n]=[6,-3,0,1,2]$ and $h[n]=$.	2022
	Determine the convolution sum of the two sequences: $x_1(n)=3,2,1,2$ and $x_2(n)=1,2,1,2$.	2021
	Determine the convolution of the sum of the two sequences: $x_1(n)=3,2,1,2,x_2(n)=1,2,1,2$.	2020
	Given two sequences of length, N=4 defined by $x_1(n)=0,1,2,3$ and $x_2(n)=1,1,2,2$. Determine their linear and periodic convolution.	2018
	Given two sequences of length N=4 defined by $x_1(n)=1,2,2,1$ and $x_2(n)=2,1,1,2$. Determine their linear and periodic convolution.	2017
	Find the output response of an FIR filter with impulse response $h(n)=1,2,-2,-1,0$ and input sequence $x(n)=1,2,3,0$ using linear convolution graphically.	2019, 2015
	Consider h(t) be the triangular pulse and x(t) be the unit impulse train as shown in Fig. 2(b). Determine $y(t)=x(t)\ast h(t)$ for T=2.	2021
Difference Equations & Block Diagrams	What are the methods of representing a system? Draw the block diagram of the system described by $\frac{d^2}{d{t}^2}y(t)+3y(t)=\frac{d}{dt}x(t)+2\frac{d^2}{d{t}^2}x(t)$.	2024, 2023, 2019
	What are the methods for representing a system? Draw the block diagram of the system described by the difference equation $y(n)+1/2y(n-1)+1/4y(n-2)=x(n-1)$.	2016
	Draw the block diagram of the system described by the difference equation $y(n)+\frac{1}{3}y(n-1)+\frac{1}{5}y(n-3)=x(n-1)$. [07/08]	2023, 2018
	Draw the block diagram for the following differential equation: $\frac{d^{2}y}{d{t}^2}+2\frac{dy}{dt}+y(t)=\frac{d^{2}x}{d{t}^2}-\frac{dx}{dt}-6x(t)$	2022
	Draw the block diagram of the system: $y(n)+0.3y(n-1)+0.25y(n-2)=x(n-1)$.	2015
	Find the output y(t) of the following LTI system. [Block Diagram: integral → y(t) → derivative → y(t)]	2024
	Find the output y(t) for the following LTI system: $x(t)\to {\int }_{-\infty }^{t}dt\to y(t)\to \frac{d}{dt}\to x(t)$. If $x(t)=u(t),t\ge 0$.	2023
	Determine and sketch the response of the system to the following inputs: i) $x_1(t)=x(t)-x(t-4)$ ii) $x_2(t)=x(t)+x(t+2)$	2021
	Obtain the impulse response and difference equation of the system if the input signal $x(n)=1,0,1,0$ and output signal $y(n)=2,3,7,0,1,0$.	2024
	Obtain the impulse response and difference equations of the system if the input signal $x(n)=2,0,5,3,0$ and the output signal $y(n)=3,5,7,0,2,1$.	2023
	Determine the impulse response for the system h(n) for the system described by the second order difference equation: $y(n)+3y(n-1)+4y(n-2)=x(n)+2x(n-1)$.	2019
	What is impulse response? Determine the impulse response for the system given by the difference equation: $y(n)+4y(n-1)+3y(n-2)=2x(n)-x(n-1)$.	2018
	What is the impulse response? Determine the impulse response for the system given by the difference equation: $y(n)+3y(n-1)+2y(n-2)=2x(n)-x(n-1)$.	2016
	Find the impulse response for the causal system $y(n)-y(n-1)=x(n)+x(n-1)$. Also find the response of the system if input is $x(n)=u(n)$.	2015
	Determine the output of the system described by the difference equation with input and initial conditions as specified: $y(n)-\frac{1}{9}y(n-2)=x(n-1)$, where $x(n)=u(n-1)$, $y(-1)=1,y(-2)=0$.	2018
	Determine the output of the system described by the difference equation with input and initial conditions as specified. $y(n)-\frac{1}{9}y(n-2)=x(n-1)$; $x(n)=u(n),y(-1)=1,y(-2)=0$.	2017
	Find the complete solution of the first order recursive system of figure 3(c), if the input is $x(n)=(\frac{1}{2}{)}^{n}u(n)$, initial condition $y(-1)=8$ and $p=\frac{1}{4}$.	2019, 2016
	Find the magnitude and phase response for the system characterized by the difference equation $y(n)=\frac{1}{6}x(n)+\frac{1}{3}x(n-1)+\frac{1}{6}x(n-2)$.	2018
	Given the $2^{nd}$ order difference equation is: $y(n)+y(n-1)+\frac{1}{4}y(n-2)=x(n)+2x(n-1)$. Find the two output values y(1) and y(2) for the system; assuming that the input is $x(n)=(\frac{1}{2}{)}^{n}u(n)$ and initial conditions are $y(-1)=1$ & $y(-2)=-2$.	2015
System Interconnection & Cascade	Consider the cascade interconnection of three causal LTI systems as shown in figure 2(c). The impulse response are given below: $h_1[n]=$, $h_2[n]=$, $h_3[n]=$ & input sequence $x[n]=$. Determine the system response of this LTI system.	2022
	Consider the system shown in Fig. 3(b) / Fig. 3(c) with h(n) being real. If $y_2(n)=y_1(n)$, find the overall impulse response $h_1(n)$ that relates $y_2(n)$ to $x(n)$.	2021, 2020
	An LTI system consists of two subsystems in cascade. The impulse responses are, respectively given in Fig. 4(a). [$h_1(t)=e^{-3t}u(t)$, $h_2(t)=e^{t}u(t)$]. Find the impulse response of the overall system.	2021
	Consider the system described by $\frac{dy(t)}{dt}+y(t)=x(t),y(0)=0$. (i) Determine the step response of the system. (ii) Determine the impulse response from the step response.	2020
	An initial relaxed LTI system was tested with an input signal $x(n)=u(n)$ and found to have a response as shown in Table 4(b). i) Obtain impulse response. ii) Deduce the differential equation.	2021

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Table 3: State-Space Representation

Subtopic	Exact Question [mark]	Year(s) of Appearance
From Differential/Difference Equations	Represent the following differential equation given below in a state model. $\frac{d^{3}y}{d{t}^3}+\frac{d^{2}y}{d{t}^2}+6\frac{dy}{dt}+7y=2u(t)$	2024
	Obtain the state-space representation of a discrete time system described by the following equation: $y(n-3)+2y(n-2)+3y(n-1)+4y(n)=U(n)$	2022
	Obtain the state-space representation of a discrete time system described by the following differential equation: $y(n-3)+2y(n-2)+3y(n-1)+4y(n)=u(n)$	2021
From Electrical Circuits	Obtain the state model for a system represented by an electrical system as shown in Fig. 2(c). [Circuit with R, C, R, C]	2025
	Represent the following electrical circuit by a state model. [L1, L2, R1, C, R2]	2024
	Obtain state space representation of the circuit shown in Fig. 3(b) considering the current through the inductor and voltage across the capacitor as state variables and voltage across the capacitor as the output y(t).	2023
	Define state of a system. Find the state variable description of the RC circuit in figure 4(a) if input is x(t) and output is current y(t) through resistor $R_1$.	2019
	Find the state variable description of the circuit in Fig. 4(b). Choose the state variables as the voltage across the capacitor and current through the inductor.	2018
	From the electrical circuit in Fig. 4(d) / Fig. 4(b), derive a state-variable description of this system if the input is applied voltage x(t) and the output is the current y(t) through the resistor $R_1$. [10/12]	2018, 2016
	Define state of a system. Find the state variable description depicted in Fig. 4(d). Chose the state variables $q_1(t)$ and $q_2(t)$ as the voltage across the capacitor and current through the inductor.	2017
From Block Diagrams	What is the state of a system? Find the state variable description corresponding to the system depicted in Fig. 4(a) by choosing the state variables to be the outputs of the unit delays.	2016
	Evaluate the state variable description corresponding to the system in figure 4(c) by choosing the state variables to be the outputs of the unit delays.	2015
Circuit Differential Equations	Given an RC series circuit in Fig. 3(c) whose input is e(t) and output is i(t). i. Obtain a difference equation describing the system. ii. How many energy storage devices are there and why? iii. Determine its homogenous solution. iv. Determine its particular solution, if $e(t)=\cos (\omega t)$. v. Determine the complete solution of the circuit to an input $e(t)=\cos (t)u(t)$ V, when R = 1$\Omega$, C = 1F & initial volatage across capacitor is $v_c(0)=3V$.	2018
	Given an RC series circuit in figure 3(c) whose input is e(t) and output is i(t). i) Obtain a differential equation describing the system response. ii) How many energy storage devices are there and why? iii) Determine its homogeneous solution. iv) Determine its particular solution, if input e(t)=cos(wt). v) Determine the complete response of the circuit to an input, $e(t)=\cos (t)u(t)$ V, when R=1$\Omega$, C=1F & initial voltage across capacitor is $v_c(0)=3$ V.	2015
	Given an RL circuit depicted in Fig. 3(c), whose input is x(t) and output is y(t). i) Obtain the differential equation describing the system. ii) Obtain the number of memory elements in the system. iii) Determine the homogeneous solution of the system. iv) Determine the particular solution of the system if input x(t)=u(t). v) Determine the complete solution of the system if initial current through the inductor is y(0) = -1A and R=1$\Omega$, L=1H.	2017

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Table 4: Fourier Analysis (Series & Transform)

Subtopic	Exact Question [mark]	Year(s) of Appearance
Fourier Series Definitions	Define Fourier series. State necessary and sufficient conditions for the existence of the Fourier series representation for a signal [08/07]	2022, 2018
	State necessary and sufficient conditions for the existence of the Fourier series representation for a signal.	2017
	What is meant by Fourier series expansion? What are the “Symmetry Conditions” of Fourier series.	2020
	What is meant by Fourier series expansion? What are the “symmetry conditions” of Fourier series?	2019
	”A periodic signal can be represented as a summation of a number of sinusoidal wave with different frequencies”-Justify the statement.	2016
	Regarding Fourier series representation, show that odd functions have only sine term coefficients.	2018
	With regard to Fourier series representation, justify that odd function have only sine term coefficients.	2017
Fourier Series Calculations	Find the Fourier series of a periodic signal x(t) with period 3 defined over the period by $x(t)=\{\begin{array}{l}t+2,-2\le t\le 02-2t,0\le t\le 1\end{array}$	2023
	Obtain the Fourier components of the periodic square wave signal which is symmetrical with respect to the vertical axis at t=0 shown in Fig. 5(b)/Fig. 5(c). [11/12]	2022, 2017
	Obtain the trigonometric Fourier series for the waveform shown below: [Triangle wave]	2021
	Obtain the Fourier components of the periodic rectangular waveform shown in Figure 4(b).	2020
	Determine the complex exponential Fourier series for the signal illustrated below: [Half-wave rectified cosine]	2021
	The complex exponential Fourier representation of a signal x(t) over period (0, T) is $x(t)={\sum }_{n=-\infty }^{\infty }\frac{3}{4+(n\pi {)}^2}{e}^{j3n\pi t}$. Determine, (i) the value of period T; (ii) what percent of energy is contained in the first five terms, if the maximum power is 0.7?	2018
Fourier Transform Fundamentals	Define Fourier transform. Briefly explain the properties of Fourier transform.	2025, 2024
	Define Fourier transform pair. Derive Fourier transform pair of Gaussian pulse.	2019
	What is Fourier transform? What are the effects in discrete spectrum if the time period (T) of a period signal f(t)?	2016
	Define the Fourier transform of a time function and explain under what condition it exits.	2015
	Briefly explain the properties of Fourier transform.	2018
	What is Signum function? Find the Fourier transform pair of this function.	2022
	What is signum function? Find the Fourier transform pair of this function.	2019
Fourier Transform Proofs & Rules	Show that the normalized Gaussian pulse is its own Fourier transform.	2024, 2018
	Show that the normalized Gaussian pulse is it’s own Fourier transform.	2017
	Show that the convolution of the signals in the time domain is equal to the multiplication of their individual Fourier transform in the frequency domain.	2022
	Show that the convolution of the signals in the time domain is equal to the multiplication of their individual Fourier transforms in the frequency domain.	2018
	Show that the time shift in the time domain is equal to a phase shift in the frequency domain.	2023
	State Parseval’s theorem and discuss on its importance in signal processing. [08/06]	2022, 2016
	State and prove Parsival’s identity for Fourier series.	2020
	State and prove Persival’s Identity for Fourier series.	2019
Calculating FT / Inverse FT	Find the Fourier transform of the time function $f(t)=5[u(t+3)+u(t+2)-u(t-2)-u(t-3)]$.	2025
	Obtain the Fourier transform of the given function: $f(t)=5[u(t+3)+u(t+2)-u(t-2)-u(t-3)]$.	2016
	Evaluate the Fourier transform of the given function, $f(t)=5[u(t+3)+u(t+2)-u(t-2)-u(t-3)]$	2015
	Determine the Fourier transform for the double exponential pulse shown in Fig. 5(c) whose function is given by $e^{-a	t
	Determine the Fourier transform for the double exponential pulse shown in Fig. 6(c), whose function is given by $f(t) = e^{-a	t
	Find the Fourier transform of the signal f(t) shown in figure 5(d). [Triangle/Trapezoid]	2019
	Derive Fourier transform pair for single pulse or transient only	2017
	Obtain the Fourier transform of the signal $f(t)=\frac{1}{2}[\delta (t+1)+\delta (t+\frac{1}{2})+\delta (t-\frac{1}{2})+\delta (t-1)]$	2017
	A certain function of time, f(t) has a Fourier transform $F(j\omega )=\frac{1}{{\omega }^2+1}{e}^{-j{\omega }^3+1}$. Write down the Fourier transform of (i) f(2t), (ii) $f(t-2)e^{jt}$, (iii) $3\frac{df(t)}{dt}$, and (iv) $\frac{f(t)}{-jt}$.	2021
	Determine the inverse Fourier transform of the spectrum shown in Fig. 5(c).	2025
	Consider the Fourier transform $X(j\Omega )$ of a signal shown in Fig. 5(b). Find the inverse Fourier transform of it.	2023
	Sketch the double-sided frequency spectrum of the signal $x(t)=10\cos (20\pi t-\pi /6),-\infty <t<\infty$.	2019
	Sketch the single and double sided frequency spectra of the following signal: $x(t)=25\cos (5\pi t-\pi /2)$	2017
	Sketch single and double-sided frequency spectra of the signal $x(t)=12\sin (5\pi t-\pi /2)$.	2018
	Draw the double side frequency spectrum of $x(t)=8\sin (20\pi t-\pi /4),-\infty <t<\infty$	2016
	What would be the energy signal of $x(t)e^{-at}u(t)$? Also determine the frequency $\omega$ so that the energy contributed by the spectrum components of all frequencies below $\omega$ is 95% of the signal energy $E_x$.	2015

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Table 5: Laplace Transform & Circuit Applications

Subtopic	Exact Question [mark]	Year(s) of Appearance
Laplace Fundamentals & Relation to FT	Determine the relationship between Laplace transform and Fourier transform.	2025
	Discuss the relationship between Laplace transform and Fourier transform.	2021
	What is the main difference between Fourier transform and Laplace transform? Find the Laplace transform of $t^n$ function. [12/10/08]	2024, 2022, 2019
	State and explain Laplace transform and its inverse transform.	2017, 2015
	Define Laplace transform. State the “Initial” and “Final” value theorems and mention their applications.	2019, 2016
	Discuss initial value and final value theorems in Laplace transform domain.	2023
	Explain the following terms in relations to Laplace transform: i) Linearity ii) Scaling, iii) Time-shift, iv) Frequency differentiation, v) Time correlation.	2015
	If x(t) is a signal with Laplace transform X(s) then prove $\frac{dX(s)}{ds}=\mathcal{L}-tx(t)$.	2023
	Find the Laplace transform of a signal sawtooth pulse shown in Fig. 7(c).	2018
Poles, Zeros, and Inverse Laplace	Draw the poles and zeros for the current I(s) in a network given $I(s)=\frac{3s}{(s+2)(s+4)}$ and hence, obtain i(t).	2025
	Draw the poles and zeros for the current I(s) in a network given by $I(s)=\frac{3s}{(s+2)(s+4)}$ and hence obtain i(t). [09/13]	2018, 2016
	Draw the poles and zeros for $V(s)=\frac{(s+1)(s+3)}{(s+2)(s+4)}$ and evaluate v(t).	2024
	Define zeros and poles. How the stability of a system is determined? [10/05/07]	2023, 2022, 2018, 2017
	Define zeros and poles in s-domain. How the stability of a system is determined?	2023
	What is transfer function? Draw the poles and zeros for the current, I(s) in a network given by $I(s)=\frac{3(s-1)}{(s+1)(s+3)}$, also obtain the current i(t) form it.	2019
	The transfer function of a system is given by $H(s)=\frac{9s}{s^2+2s+2}$. Plot the pole-zero diagram and hence determine h(t).	2020
	Determine the inverse Laplace transform of $F(s)=\frac{2s^2+3s+3}{(s+1)(s+3{)}^2}$. Draw the pole-zero diagram for the given function.	2016, 2015
Circuit Applications (s-domain)	In the circuit of Fig.6(c), find the currents $i_1(t)$ and $i_2(t)$ and output voltage across $5\Omega$ resistor when the switch is closed, and also determine the initial and final value of current.	2025
	In the circuit of Fig. 7(c), (i) find the current $i_1(t)$ and $i_2(t)$ and the output voltage across 5$\Omega$ resistor when the switch is closed, and (b) also determine the initial and final values of current.	2016
	In the circuit of Fig. 6 (c) the switch S is closed and steady-state conditions have been reached. At t = 0, the switch S is opened. Obtained the expression for the current through the inductor.	2024
	In the circuit shown in Fig. 7(c), find the current i(t) when the switch is at position 2. The switch s is moved from position 1 to position 2 at time t = 0. Initially the switch has been at position 1 for a long time.	2023
	In the circuit drawn below, find the current i(t) when the switch is at position 2. The switch S moved from position 1 to position 2 at time t=0. Initially the switch has been at position 1 for a long time. [Circuit 10V, 5ohm, 5ohm, 2H]	2021
	For the circuit shown in Fig. 7(d), determine the current i(t) when the switch is at position 2. The switch S is moved from position 1 to 2 at time t=0. Initially the switch has been at position 1 for a long time.	2018
	For the circuit shown in Fig. 7(d), determine the resultant current i(t) when the switch is moved from position 1 to position 2 at t=0. Initially the switch has been at position 1 for a long time to get the steady state values.	2017
	In a series RLC circuit shown in Fig. 6(d) there is no initial charge on the capacitor. If the switch is closed at t=0, find the resulting current.	2022
	In the series RLC circuit shown in Fig. 5(c), find the resulting current i(t), when the switch is closed at t=0. There is no initial charge on the capacitor.	2020
	In the circuit of figure 7(c), find the resulting current i(t), when the switch is closed at t=0. There is no initial charge on the capacitor.	2019
	In the series RL circuit shown in Fig. 7(b), find the current i(t) & draw its s-domain equivalent circuit.	2016
	Obtain $v_o(t)$ using loop equation from the following circuit in figure 6(c).	2019
	Obtain $v_o(t)$ using loop equation from following circuit as shown in figure 7(c)	2015
	Draw s-domain circuit from circuit figure 6(d) and also obtain $v_o(t)$ for $t>0$.	2019
	Draw s-domain circuit from circuit of the figure 7(d) and also determine $v_o(t),t>0$.	2015
	Consider the parallel RLC circuit in Fig. 7(d) with R=1 $\Omega$ and L=1 H. i) Determine the differential equation relating $I_s,I_L$. ii) Obtain zero-state response for $I_L(t)$ using Laplace transform for $I_s(t)=e^{-3t}u(t)$.	2021

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Table 6: Z-Transform & Discrete-Time Analysis

Subtopic	Exact Question [mark]	Year(s) of Appearance
Z-Transform Fundamentals & ROC	How is z-transform obtained from Laplace transform? [06/05/08]	2024, 2019, 2017, 2015
	Define z-transform. Write down some properties of z-transform.	2022
	Mention some properties of z-transform.	2021
	Define Z-transform and Inverse Z-transform. Determine the Z-transform of the signal, $x(n)=\delta (n+1)+3\delta (n)+7\delta (n-3)-3\delta (n-4)$.	2018
	Define z-transform. What are the applications of z-transform in signal & system analysis?	2016
	What are the properties of Region of convergence?	2024
	Explain region of convergence of a rational z-transform.	2021
	Briefly discuss the properties of two sided Z-transform and compare them with one sided Z-transform.	2020
	What is region of convergence? Write down some properties of z-transform.	2019
	What is region of convergence? Explain it with example.	2018
	What is region of convergence? Explain it with an example.	2017
	What is region of convergence? Describe the properties of region of convergence (ROC) with proper illustration.	2015
Calculating Z-Transform	Find the z-transform of the sequence $x(n)=[u(n)-u(n-5)]$ and its ROC.	2025
	Determine the z-transform of the following signals: i) $x(n)=2,4,6,8,1,3,7$ ii) $x(n)=u(n-k)$ iii) $x(n)=\delta (n-5)+\delta (n+3)$	2023
	Determine the z-transform of the following signal: i) $x(n)=\delta (n+1)+3\delta (n)+7\delta (n-3)-3\delta (n-4)$ ii) $(-\frac{1}{3}{)}^{n}u(-n)$	2022
	Determine the z-transform for the following signals: i) $x(n)=\delta (n+1)+3\delta (n)+6\delta (n-3)$ ii) $x(n)=2,4,5,7,0,1,2$ iii) $x(n)=u(-n)$	2021
	Determine the z-transform for the following signals: i. $x(n)=2,4,5,7,6,1,2$ ii. $x(n)=\delta (n-k)$ iii. $x(n)=u(n-k)$	2016
	Determine the z-transform of the following sequences: i) $\delta (n-5)$, ii) $e^{jn\pi /4}u(n)$, iii) $(1/3{)}^{n}u(-n)$.	2017
	Find the Z-transform of the following discrete time signal including the region of convergence. $x(n)=e^{-4n}u(n-1)$	2020
Inverse Z-Transform	Determine the inverse z-transform of the system function $H(z)=\frac{z^2-3z+8}{(z-2)(z+2)(z+3)}$.	2024
	If x(n) is causal, find the inverse z-transform of $X(z)=\frac{1}{z(z-0.8)(z+0.4)}$.	2023
	By applying time shifting property, determine the inverse z-transform of the following system $X(z)=\frac{z^{-1}}{1-3z^{-1}}$	2022
	By applying time shifting property, determine the inverse Z-transform of the system $X(z)=\frac{z^{-1}}{1-3z^{-1}}$.	2018
	By applying the time shifting property, determine the inverse z-transform of the signal $X(z)=\frac{z^{-1}}{1-3z^{-1}}$.	2017
	Assuming the sequence x(n) to be right-sided, find the inverse z-transform of the following: $X(z)=\frac{z}{(z-a)(z-b)}$	2021
	Determine the inverse Z-transform of the following X(z) by the partial fraction expansion method. $X(z)=\frac{(z-0.5)}{z(z-0.8)(z-1)}$	2020
	Using the residue method, find the inverse Z-transform of $X(z)=\frac{1}{(z-0.2)(z-0.9)}$.	2019
	Find the inverse Z-transform of $H(z)=\frac{-4+8z^{-1}}{1+6z^{-1}+8z^{-2}}$.	2018
	Find the signal x(n) having the z-transform: $X(z)=\frac{-4+8z^{-1}}{1+6z^{-1}+8z^{-2}}$	2022
	Determine the inverse z-transform of $X(z)=\frac{z}{3z^2-4z+1}$ if the region of convergence are i) $	z
	Determine the casual signal x(n) having the z-transform $X(z)=\frac{1}{(1+z^{-1})(1-z^{-1}{)}^2}$	2016
	Determine x(n) for X(z) given by $X(z)=\frac{z-0.5}{z(z-0.8)(z-1)}$	2015
Initial & Final Values	If $X(z)=2+3z^{-1}+4z^{-2}$, find the initial and final values of the corresponding sequence, x(n).	2025
	If $X(z)=2+3z^{-1}+4z^{-2}$, find the initial and final values of the corresponding sequence x(n).	2020
	If $X(z)=2+3z^{-1}+4z^{-2}$, find the initial and final values of the corresponding sequence. [05/06]	2022, 2019
	Prove that the final values of x(n) for $X(z)=\frac{z^2}{(z-1)(z-0.2)}$ is 1.25 and its initial value is unity. [10/07]	2024, 2019, 2015
	Find the initial and final values of the function $F(s)=\frac{17s^3+7s^2+s+6}{s^5+3s^4+5s^3+4s^2+2s}$.	2021
System Function & Z-domain Analysis	Find the impulse response of a system described the following difference equation: $y(n)-\frac{5}{6}y(n-1)+\frac{1}{6}y(n-2)=\frac{1}{3}x(n-1)$	2025
	A system is described by the difference equation $y(n)+y(n-1)=x(n)$, y(n)=0, for n<0. i) Determine the transfer function and discuss the stability of the system. ii) Determine impulse response h(n) and show that it behaves according to the conclusion drawn from (i). iii) Determine the response when x(n)=10 for $n\ge 0$. Assume that the system is initially relaxed.	2021
	A system has an impulse response $h(n)=1,2,3$ and output response $y(n)=1,1,2,-1,3$. Determine the input sequence x(n) using z-transform.	2023
	Find the convolution and correlation of the two sequences $x(n)=3,1,0,1,5$ and $h(n)=1,2,4,1$. [12/10]	2024, 2018
	Determine the convolution and cross correlation of the two sequence using z-transform. $x(n)=1,2,3,4$; $y(n)=1,1,1,1$	2022
	Determine the cross-correlation sequence $r_{x_1{x}_2}(l)$ of the sequences are $x_1(n)=(1,2,3,4)$, and $x_2(n)=(2,3,4,5)$.	2025
	Define and explain cross correlation and auto-correlation of sampled signals.	2015
	Define transfer function. Discuss the concept of transfer function and its application in z-transform.	2022
	Explain transfer function and explain its significance in circuit analysis.	2021
	Discuss the concept of transfer function and its application.	2015
	Determine the convolution and correlation of the two sequences $x(n)=1,0,1,0,5$ and $h(n)=1,1,2,2$.	2016

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Table 7: Sampling, Filters & Network Theory

Subtopic	Exact Question [mark]	Year(s) of Appearance
Sampling & Aliasing	What is sampling theorem? Find out the up-sampling sequence $x_u(n)$ and down-sampling sequence $x_d(n)$ from the input signal sequence $x(n)=$ for the discrete time system. [3+7]	2024
	What is the sampling theorem? Draw the block diagram of analog-to-digital conversion process.	2023
	What is sampling theorem?	2022
	What is discrete time up-sampler and down-sampler? If $x[n]=[2,6,0,3,1,2,...]$, then find the compressed and expanded signal of x[n] by down-sampler 3 and up-sampler 3.	2022
	Define (i) Discrete time up-sampler; (ii) Discrete time down-sampler.	2021
	Explain aliasing effect and the means to avoid it.	2021
	What is meant by aliasing effect and what are the means to avoid it?	2019
	State and prove the Shannon-Nyquist sampling theorem. [10/08]	2019, 2017
	State and prove Shannon-Nyquist sampling theorem. Classify the sampling techniques.	2018
	State sampling theorem. Write short notes on : (i) Over-sampling, (ii) Nyquist rate sampling, (iii) Aliasing	2016
	Write short notes on (i) over-sampling, (ii) aliasing.	2018
	Distinguish between Ideal, Natural, and Flat-top sampling techniques.	2017
	i) State sampling theorem; ii) Show the criteria and frequency spectrum in case over-sampling, under-sampling & Nyquist rate sampling; iii) Explain aliasing effect and anti-aliasing filter briefly. [03+04+04]	2015
Analog Filters (Butterworth/Elliptic)	Design a Butterworth low pass filter with 1dB passband ripple, passband edge frequency ${\Omega }_p=2000\pi$ rad/Sec, stop band edge frequency ${\Omega }_s=10,000\pi$ rad/Sec, and a minimum stop band ripple of 40dB.	2025
	Design a Butterworth analog low pass filter with 1 dB passband ripple, passband edge frequency ${\Omega }_p=2000\pi$ rad/sec, stopband edge frequency ${\Omega }_s=10000\pi$ rad/sec, and a minimum stopband ripple of 40 dB. [Use table as per instruction]	2023
	Design a elliptic LPF with: $f_p=1kHz,f_s=1.5kHz,A_p=1dB,A_s=40dB$. Determine (i) order, n; (ii) ripple factor $ϵ$; (iii) Transfer function.	2025
	Draw the specifications for analog low pass filter with tolerance curve.	2024
	Determine the impulse response h(n) of low pass filter.	2024
	What is filtering? What are the applications of it?	2023
	In the system shown below, determine the output response of the low pass RC network for an input signal, $x(t)=e^{-t/RC}$.	2021
	In the system shown in Fig. 5(d), determine the output response of the low-pass RC network for an input signal $x(t)=e^{-t/RC}$.	2017
	Determine the output response y(t) of the RC low-pass network shown in Fig. 6(b) due to an input $x(t)=t{e}^{-t/RC}$ by convolution.	2016
	The input signal $x(t)=e^{-at}u(t),a>0$ is applied to the system whose transfer function is $h(t)=e^{-bt}u(t),b>0$. Determine the output signal y(t) when $b\ne a$ and $b=a$.	2017
Two-Port Networks	What in network theory? Classify the two-port network.	2025
	What is network theory? Classify the two port network.	2022
	What do you mean by two-port network? Obtain ABCD parameters for the following network: [T network 1 ohm, 2 ohm, 5 ohm] [4+8]	2024
	Determine the ABCD matrix for the two-port between as shown in Fig. 4(b). [Pi/T network]	2025
	Determine the ABCD matrix for the two port network shown in Fig. 4(c) [10 ohm, 10 ohm, 50 ohm T network]	2022
	For the following $\Pi$-network as shown in Fig. 4(c), find the Y-parameters of it.	2025
	Find the Z & Y parameters of two port network shown in Fig. 4(b). [24 ohm, 8 ohm, 8 ohm T network]	2022

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Table 8: DFT & Fast Fourier Transform (FFT)

Subtopic	Exact Question [mark]	Year(s) of Appearance
FFT Concepts	What is DIT-FFT algorithm? Give the computation efficiency of FFT over DFT.	2025
	What is FFT algorithm? Give the computation efficiency of FFT over DFT.	2023
	Why is FFT called so? How can you compute IDFT using FFT algorithm.	2024
FFT/DFT Calculation	Given, $x(n)=n^2$ and $N=8$, Find X(k) using DIF-FFT algorithm.	2025
	Given $x(n)=n+1$ and $N=8$. Find X(k) using DIF FFT algorithm.	2023
	Given $x(n)=0,1,2,3$. Find X(k) using DIT-FFT algorithm.	2024