signal checklist

Instructor 1: Transform Techniques (Fourier, Laplace, Z-Transform, FFT)

1. Fourier Series

• Define the term “Fourier series” and explain its fundamental purpose. [PYQ: 2022, 2018, 2017] [Heavily Tested]
• Explain what is meant by “Fourier series expansion”. [PYQ: 2020, 2019]
• Define the “Symmetry Conditions” of a Fourier series. [PYQ: 2020, 2019]
• State the necessary and sufficient conditions (Dirichlet conditions) for the existence of the Fourier series representation for a signal. [PYQ: 2022, 2018, 2017] [Heavily Tested]
• Prove that a periodic signal can be represented as a summation of a number of sinusoidal waves with different frequencies. [PYQ: 2016]
• Prove that odd functions have only sine term coefficients in their Fourier series representation. [PYQ: 2018, 2017]
• State and prove Parseval’s identity for Fourier series. [PYQ: 2020, 2019]
• Calculate the Fourier series of a periodic signal $x(t)$ with period 3 defined piecewise as $t+2$ for $-2\le t\le 0$ and $2-2t$ for $0\le t\le 1$. [PYQ: 2023]
• Calculate the Fourier components of a periodic square wave signal which is symmetrical with respect to the vertical axis at $t=0$. [PYQ: 2022, 2017]
• Calculate the trigonometric Fourier series for a triangular waveform. [PYQ: 2021]
• Calculate the Fourier components of a periodic rectangular waveform. [PYQ: 2020]
• Calculate the complex exponential Fourier series for a half-wave rectified cosine signal. [PYQ: 2021]
• Solve for the value of period $T$ given the complex exponential Fourier representation: $x(t)=\sum \frac{3}{4+(n\pi {)}^2}{e}^{j3n\pi t}$. [PYQ: 2018]
• Calculate the percent of energy contained in the first five terms of a Fourier series if the maximum power is 0.7. [PYQ: 2018]
• Explain the exponential form of the Fourier series.
• Explain the concept of orthogonality and orthonormality of signals.

2. Fourier Transform

• Define the Fourier transform of a time function. [PYQ: 2025, 2024, 2016, 2015] [Heavily Tested]
• Define what a “Fourier transform pair” is. [PYQ: 2019]
• Explain under what conditions the Fourier transform of a signal exists. [PYQ: 2015]
• Define the Signum function mathematically. [PYQ: 2022, 2019]
• Explain the properties of the Fourier transform (Linearity, Time-shift, Modulation, etc.). [PYQ: 2025, 2024, 2018] [Heavily Tested]
• Explain the effects on the discrete spectrum if the time period ($T$) of a periodic signal changes. [PYQ: 2016]
• State Parseval’s theorem for Fourier transforms. [PYQ: 2022, 2016]
• Explain the importance and applications of Parseval’s theorem in signal processing. [PYQ: 2022, 2016]
• Differentiate between the Fourier transform and the Laplace transform in a comparison table. [PYQ: 2024, 2022, 2021, 2019] [Heavily Tested]
• Prove that the normalized Gaussian pulse is its own Fourier transform. [PYQ: 2024, 2018, 2017] [Heavily Tested]
• Prove that the convolution of signals in the time domain is equal to the multiplication of their individual Fourier transforms in the frequency domain. [PYQ: 2022, 2018]
• Prove that a time shift in the time domain is equal to a phase shift in the frequency domain. [PYQ: 2023]
• Derive the Fourier transform pair for a single pulse or transient. [PYQ: 2017]
• Derive the Fourier transform pair of a Gaussian pulse. [PYQ: 2019]
• Derive the Fourier transform pair of the Signum function. [PYQ: 2022, 2019]
• Calculate the Fourier transform of the time function $f(t)=5[u(t+3)+u(t+2)-u(t-2)-u(t-3)]$. [PYQ: 2025, 2016, 2015] [Heavily Tested]
• Calculate the Fourier transform for the double exponential pulse $e^{-a|t|}$. [PYQ: 2024, 2018]
• Calculate the Fourier transform of a triangular/trapezoidal signal $f(t)$. [PYQ: 2019]
• Calculate the Fourier transform of the signal $f(t)=\frac{1}{2}[\delta (t+1)+\delta (t+\frac{1}{2})+\delta (t-\frac{1}{2})+\delta (t-1)]$. [PYQ: 2017]
• Apply Fourier transform properties to find the FT of $f(2t)$, $f(t-2)e^{jt}$, $3\frac{df(t)}{dt}$, and $\frac{f(t)}{-jt}$ given $F(j\omega )=\frac{1}{{\omega }^2+1}{e}^{-j{\omega }^3+1}$. [PYQ: 2021]
• Calculate the inverse Fourier transform from a given frequency spectrum diagram. [PYQ: 2025, 2023]
• Sketch the single and double-sided frequency spectra of the signal $x(t)=25\cos (5\pi t-\pi /2)$. [PYQ: 2017]
• Sketch the single and double-sided frequency spectra of the signal $x(t)=12\sin (5\pi t-\pi /2)$. [PYQ: 2018]
• Draw the double-sided frequency spectrum of $x(t)=10\cos (20\pi t-\pi /6)$. [PYQ: 2019]
• Draw the double-side frequency spectrum of $x(t)=8\sin (20\pi t-\pi /4)$. [PYQ: 2016]
• Solve for the energy signal of $x(t)e^{-at}u(t)$. [PYQ: 2015]
• Calculate the frequency $\omega$ so that the energy contributed by the spectrum components below $\omega$ is 95% of the total signal energy $E_x$. [PYQ: 2015]
• Explain Energy Spectral Density (ESD) and Power Spectral Density (PSD).

3. Laplace Transform & Circuit Applications

• Define the Laplace transform and its inverse transform. [PYQ: 2019, 2017, 2016, 2015] [Heavily Tested]
• Define zeros and poles in the s-domain. [PYQ: 2023, 2022, 2018, 2017] [Heavily Tested]
• Define the concept of a “transfer function” in circuit analysis. [PYQ: 2019]
• State the “Initial Value Theorem” and “Final Value Theorem” in the Laplace transform domain. [PYQ: 2023, 2019, 2016] [Heavily Tested]
• List the practical applications of the Initial and Final Value theorems. [PYQ: 2019, 2016]
• Explain the following properties of Laplace transform: Linearity, Scaling, Time-shift, Frequency differentiation, Time correlation. [PYQ: 2015]
• Explain how the stability of a system is determined using poles and zeros. [PYQ: 2023, 2022, 2018, 2017] [Heavily Tested]
• Prove the differentiation property: $\frac{dX(s)}{ds}=\mathcal{L}-tx(t)$. [PYQ: 2023]
• Calculate the Laplace transform of the $t^n$ function. [PYQ: 2024, 2022, 2019] [Heavily Tested]
• Calculate the Laplace transform of a given sawtooth pulse signal. [PYQ: 2018]
• Calculate the inverse Laplace transform of $F(s)=\frac{2s^2+3s+3}{(s+1)(s+3{)}^2}$. [PYQ: 2016, 2015]
• Draw the pole-zero diagram for the transfer function $H(s)=\frac{9s}{s^2+2s+2}$ and solve for $h(t)$. [PYQ: 2020]
• Draw the poles and zeros for $I(s)=\frac{3s}{(s+2)(s+4)}$ and solve for the current $i(t)$. [PYQ: 2025, 2018, 2016] [Heavily Tested]
• Draw the poles and zeros for $V(s)=\frac{(s+1)(s+3)}{(s+2)(s+4)}$ and solve for $v(t)$. [PYQ: 2024]
• Draw the poles and zeros for $I(s)=\frac{3(s-1)}{(s+1)(s+3)}$ and solve for the current $i(t)$. [PYQ: 2019]
• Draw the s-domain equivalent circuit for a given series RL/RC/RLC circuit. [PYQ: 2019, 2016, 2015] [Heavily Tested]
• Solve for currents $i_1(t)$ and $i_2(t)$, the output voltage, and initial/final current values when a switch is closed in a given circuit. [PYQ: 2025, 2016]
• Solve for the inductor current expression when steady-state switch $S$ is opened at $t=0$. [PYQ: 2024]
• Solve for the transient current $i(t)$ when a switch moves from position 1 to position 2 at $t=0$ with initial conditions considered. [PYQ: 2023, 2021, 2018, 2017] [Heavily Tested]
• Solve for the resulting current $i(t)$ in a series RLC circuit when the switch is closed at $t=0$ (assuming no initial charge). [PYQ: 2022, 2020, 2019] [Heavily Tested]
• Formulate the loop equation and obtain $v_o(t)$ for a given complex circuit diagram. [PYQ: 2019, 2015]
• Determine the differential equation relating $I_s$ and $I_L$ for a parallel RLC circuit. [PYQ: 2021]
• Calculate the zero-state response for $I_L(t)$ using Laplace transform for an input $I_s(t)=e^{-3t}u(t)$. [PYQ: 2021]

4. Z-Transform & DFT/FFT

• Define the z-transform and inverse z-transform. [PYQ: 2022, 2018, 2016]
• Define the Region of Convergence (ROC) in the context of z-transforms. [PYQ: 2024, 2019, 2018, 2017, 2015] [Heavily Tested]
• Define cross-correlation and auto-correlation of sampled signals. [PYQ: 2015]
• Define the DIT-FFT and DIF-FFT algorithms. [PYQ: 2025, 2023]
• Explain the process of obtaining the z-transform from the Laplace transform. [PYQ: 2024, 2019, 2017, 2015] [Heavily Tested]
• Explain the properties of the z-transform. [PYQ: 2022, 2021, 2019]
• Explain the properties of the Region of Convergence (ROC) with proper illustrations. [PYQ: 2024, 2021, 2015]
• Compare the properties of the two-sided z-transform with the one-sided z-transform. [PYQ: 2020]
• Explain the applications of the z-transform in signal & system analysis. [PYQ: 2016]
• Explain the concept of the transfer function and its significance in z-domain circuit analysis. [PYQ: 2022, 2021, 2015]
• Explain why FFT is called the “Fast” Fourier Transform. [PYQ: 2024]
• Compare the computational efficiency of FFT over standard DFT. [PYQ: 2025, 2023]
• Prove that the final value of $x(n)$ for $X(z)=\frac{z^2}{(z-1)(z-0.2)}$ is 1.25 and its initial value is unity. [PYQ: 2024, 2019, 2015] [Heavily Tested]
• Calculate the z-transform and ROC of $x(n)=[u(n)-u(n-5)]$. [PYQ: 2025]
• Calculate the z-transform of arbitrary finite sequences (e.g., $x(n)=2,4,6,8,1,3,7$). [PYQ: 2023, 2021, 2016] [Heavily Tested]
• Calculate the z-transform of shifted impulses: $x(n)=\delta (n+1)+3\delta (n)+7\delta (n-3)-3\delta (n-4)$. [PYQ: 2022, 2021, 2018, 2017] [Heavily Tested]
• Calculate the z-transform of shifted step functions $u(n-k)$ and reversed step functions $u(-n)$. [PYQ: 2023, 2021, 2016]
• Calculate the z-transform of exponential sequences: $(-\frac{1}{3}{)}^{n}u(-n)$ and $e^{jn\pi /4}u(n)$. [PYQ: 2022, 2017]
• Calculate the z-transform and ROC of $x(n)=e^{-4n}u(n-1)$. [PYQ: 2020]
• Calculate the inverse z-transform of $H(z)=\frac{z^2-3z+8}{(z-2)(z+2)(z+3)}$ using partial fractions. [PYQ: 2024]
• Calculate the inverse z-transform of $X(z)=\frac{1}{z(z-0.8)(z+0.4)}$ assuming a causal signal. [PYQ: 2023, 2020, 2015] [Heavily Tested]
• Calculate the inverse z-transform of $X(z)=\frac{z^{-1}}{1-3z^{-1}}$ using the time-shifting property. [PYQ: 2022, 2018, 2017] [Heavily Tested]
• Calculate the inverse z-transform of $X(z)=\frac{z}{(z-a)(z-b)}$ assuming a right-sided sequence. [PYQ: 2021]
• Calculate the inverse z-transform of $X(z)=\frac{1}{(z-0.2)(z-0.9)}$ using the residue method. [PYQ: 2019]
• Calculate the inverse z-transform of $H(z)=\frac{-4+8z^{-1}}{1+6z^{-1}+8z^{-2}}$. [PYQ: 2022, 2018]
• Calculate the inverse z-transform of $X(z)=\frac{z}{3z^2-4z+1}$ for three different given ROC conditions. [PYQ: 2017]
• Calculate the inverse z-transform of $X(z)=\frac{1}{(1+z^{-1})(1-z^{-1}{)}^2}$ for a causal signal. [PYQ: 2016]
• Calculate the initial and final values of $x(n)$ given $X(z)=2+3z^{-1}+4z^{-2}$. [PYQ: 2025, 2022, 2020, 2019] [Heavily Tested]
• Calculate the impulse response $h(n)$ for the difference equation $y(n)-\frac{5}{6}y(n-1)+\frac{1}{6}y(n-2)=\frac{1}{3}x(n-1)$. [PYQ: 2025]
• Determine the transfer function, stability, impulse response $h(n)$, and step response for the system $y(n)+y(n-1)=x(n)$ using z-transforms. [PYQ: 2021]
• Solve for the input sequence $x(n)$ using z-transform given $h(n)=1,2,3$ and $y(n)=1,1,2,-1,3$. [PYQ: 2023]
• Calculate the convolution and correlation of two sequences (e.g., $x(n)=3,1,0,1,5$ and $h(n)=1,2,4,1$) using z-transforms. [PYQ: 2024, 2022, 2018, 2016] [Heavily Tested]
• Calculate the cross-correlation sequence $r_{x_1{x}_2}(l)$ for $x_1(n)=(1,2,3,4)$ and $x_2(n)=(2,3,4,5)$. [PYQ: 2025]
• Calculate an N-point DFT using the DIF-FFT algorithm (e.g., given $x(n)=n^2$ or $x(n)=n+1$, with $N=8$). [PYQ: 2025, 2023]
• Calculate an N-point DFT using the DIT-FFT algorithm (e.g., given $x(n)=0,1,2,3$). [PYQ: 2024]
• Apply the IDFT process using the FFT algorithm. [PYQ: 2024]

Sources: Syllabus pg 1 (Instructor 1 scope), Notes (Azmat Sir-2309008.pdf, 01 Fourier Series.pdf, 02 Fourier Transform.pdf, 03 Laplace.pdf, 04 Z-transform.pdf, 05 DFT FFT.pdf), PYQ 2015-2025.

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Instructor 2: Signals, Systems, Filters, and Network Theory

1. Basic Signals & Classifications

• Define “Signal” and “System”. [PYQ: 2025, 2024, 2023, 2021, 2020, 2019, 2018, 2017, 2016, 2015] [Heavily Tested] (Note 1.01)
• Define unit step, unit impulse, ramp, and signum functions. [PYQ: 2022] (Note 1.01)
• Explain the importance of signals and systems in communication engineering. [PYQ: 2024] (Note 1.01)
• Write a short note on memoryless systems. [PYQ: 2024, 2016]
• Write a short note on recursive systems. [PYQ: 2024, 2016]
• Write a short note on invertible systems. [PYQ: 2016]
• Distinguish between deterministic and non-deterministic signals. [PYQ: 2018] (Note 1.03)
• Distinguish between even and odd signals. [PYQ: 2018] (Note 1.04)
• Classify signals based on major criteria (Continuous/Discrete, Analog/Digital, Energy/Power, etc.). [PYQ: 2021, 2020, 2019, 2018, 2016, 2015] [Heavily Tested] (Note 1.03, 1.04)
• Explain the operations performed on the independent variables in the processing of discrete signals (shifting, scaling, reversal) mathematically and graphically. [PYQ: 2019, 2018, 2017, 2015] [Heavily Tested] (Note 1.02)
• Prove that the total energy of a signal is the sum of the energies of its even and odd parts: $\int x^2(t)dt=\int x_e^2(t)dt+\int x_o^2(t)dt$. [PYQ: 2024, 2023, 2021] [Heavily Tested] (Note 1.04)
• Calculate whether a given piecewise or trigonometric signal is an energy or power signal, and find its exact energy/power value. [PYQ: 2025, 2023, 2019, 2018, 2017, 2016, 2015] [Heavily Tested] (Note 1.04)
• Calculate the power and energy of the CT signal $x(t)=u(t)$. [PYQ: 2022] (Note 1.04)
• Calculate the fundamental period and energy of a composite signal like $x(t)=\sin \sqrt{2}\pi t+\sin 15\pi t$. [PYQ: 2019, 2015] (Note 1.03, 1.04)
• Determine if a composite trigonometric signal is periodic, and calculate its fundamental period. [PYQ: 2025, 2019, 2017, 2016] [Heavily Tested] (Note 1.03)
• Calculate the even and odd components for specific signals (e.g., $u(t)$, $e^{-\alpha t}u(t)$, $\cos (20\pi t-5\pi )$). [PYQ: 2020, 2019, 2018, 2015] [Heavily Tested] (Note 1.04)
• Draw/Sketch composite continuous and discrete-time signals incorporating shifting, scaling, and reversal (e.g., $x(t)=-4r(3t-1)$, $2r(0.5t+0.25)$). [PYQ: 2024, 2019, 2017, 2016, 2015] [Heavily Tested] (Note 1.02)
• Draw/Sketch piecewise unit step combinations (e.g., $t^2[u(t-1)-u(t-2)]$, $u(t-5)-u(t-7)$). [PYQ: 2021] (Note 1.02)
• Formulate the mathematical equation for a sketched signal using addition and multiplication of unit step functions. [PYQ: 2015]

2. System Properties & Stability

• Define the properties of a system. [PYQ: 2025, 2024, 2023, 2019, 2018, 2016] [Heavily Tested]
• Distinguish between causal and non-causal systems. [PYQ: 2015]
• Distinguish between FIR and IIR systems. [PYQ: 2015]
• Distinguish between linear and non-linear systems. [PYQ: 2017]
• Distinguish between recursive and non-recursive systems. [PYQ: 2017]
• Explain the characterization of discrete-time systems. [PYQ: 2023]
• Deduce the necessary and sufficient condition for Bounded Input Bounded Output (BIBO) stability of an LTI system. [PYQ: 2017, 2016, 2015] [Heavily Tested]
• Explain the process of determining system stability. [PYQ: 2021]
• Test specific signals (e.g., $e^{-2t}u(t)$, $tu(t)$) to determine if they are causal, anticausal, or noncausal. [PYQ: 2025, 2020] (Note 1.04)
• Test a continuous-time system equation (e.g., $y(t)=3x(-t)+2x(t)$) for time invariance. [PYQ: 2025, 2022]
• Test a discrete-time difference equation (e.g., $y(n)=3y(n-1)-n^{2}x(n)\dots$) to determine if it is time invariant, linear, and causal. [PYQ: 2024, 2019, 2018, 2017, 2015] [Heavily Tested]
• Test a continuous-time differential equation (e.g., $\frac{dy}{dt}+3y(t)=x(t)\frac{dx(t)}{dt}$) to determine if it is linear or nonlinear. [PYQ: 2022, 2020, 2016]
• Test the BIBO stability of a given system (e.g., $y(n)=ax(n+1)+bx(n-1)$, $y(n)=e^{-x(n)}$). [PYQ: 2020, 2019, 2017, 2015] [Heavily Tested]

3. Convolution & Time-Domain System Analysis

• Define “Impulse Response”. [PYQ: 2018, 2016]
• Explain the methods used for representing a system. [PYQ: 2024, 2023, 2019, 2016] [Heavily Tested]
• Prove that the output response of an LTI system is the convolution sum of the input signal and impulse response. [PYQ: 2023, 2017, 2015] [Heavily Tested]
• Prove that if $y(t)=x(t)\ast h(t)$, then $y(2t)=2x(2t)\ast h(2t)$. [PYQ: 2025, 2022]
• Derive the expression of convolution for a delayed input and delayed impulse response. [PYQ: 2021]
• Calculate the linear and periodic convolution sum of two discrete sequences (e.g., $x_1=3,2,1,2$, $x_2=1,2,1,2$). [PYQ: 2022, 2021, 2020, 2018, 2017, 2015] [Heavily Tested]
• Calculate the continuous-time convolution integral $y(t)=x(t)\ast h(t)$ graphically for a triangular pulse and an impulse train. [PYQ: 2021]
• Draw the block diagram representation for a system described by a differential or difference equation. [PYQ: 2024, 2023, 2022, 2019, 2018, 2016, 2015] [Heavily Tested]
• Solve for the output $y(t)$ of an LTI system defined by an integral/derivative block diagram for a given step input. [PYQ: 2024, 2023]
• Sketch the response of a system to composite inputs like $x(t)-x(t-4)$. [PYQ: 2021]
• Calculate the impulse response and formulate the difference equation given specific input $x(n)$ and output $y(n)$ signal arrays. [PYQ: 2024, 2023, 2019, 2018, 2016, 2015] [Heavily Tested]
• Calculate the complete solution of a recursive system difference equation subjected to specific initial conditions and step/exponential inputs. [PYQ: 2019, 2018, 2017, 2016, 2015] [Heavily Tested]
• Solve for the magnitude and phase response for a system characterized by a difference equation. [PYQ: 2018]
• Calculate the overall system response for a cascade interconnection of multiple causal LTI systems given their impulse responses. [PYQ: 2022, 2021, 2020]

4. State-Space Representation & Differential Equations

• Define the “state” of a system. [PYQ: 2019, 2017, 2016]
• Formulate the state-space model/matrix representation from a given 3rd-order differential equation. [PYQ: 2024, 2021]
• Formulate the state-space representation of a discrete-time difference equation. [PYQ: 2022]
• Formulate the state variable description (matrices A, B, C, D) for given electrical circuits (RC, RL, RLC networks). [PYQ: 2025, 2024, 2023, 2019, 2018, 2017, 2016] [Heavily Tested]
• Formulate the state variable description corresponding to a block diagram by choosing state variables at the outputs of unit delays. [PYQ: 2016, 2015]
• Derive the governing differential equation for a given RC/RL circuit. [PYQ: 2018, 2017, 2015] [Heavily Tested]
• Determine the number of energy storage elements (memory elements) in an RC/RL circuit and explain why. [PYQ: 2018, 2017, 2015] [Heavily Tested]
• Calculate the homogeneous solution for a circuit’s differential equation. [PYQ: 2018, 2017, 2015] [Heavily Tested]
• Calculate the particular solution for a circuit’s differential equation given a sinusoidal or step input. [PYQ: 2018, 2017, 2015] [Heavily Tested]
• Calculate the complete time-domain response of a circuit given specific resistance, inductance/capacitance values, and initial conditions. [PYQ: 2018, 2017, 2015] [Heavily Tested]

5. Sampling, Aliasing & Analog Filters

• Define the “Sampling theorem” / “Shannon-Nyquist Sampling Theorem”. [PYQ: 2024, 2023, 2022, 2020, 2019, 2018, 2017, 2016, 2015] [Heavily Tested] (Note 1.05)
• State and prove the Shannon-Nyquist sampling theorem. [PYQ: 2019, 2018, 2017] [Heavily Tested] (Note 1.05)
• Define discrete time up-sampler and down-sampler. [PYQ: 2022, 2021] (Note 1.02, 1.05)
• Explain the concept of “Filtering” and list its applications. [PYQ: 2023]
• Explain the “aliasing effect” and describe the means/filters used to avoid it. [PYQ: 2021, 2019, 2018, 2016, 2015] [Heavily Tested] (Note 1.05)
• Write short notes on over-sampling and Nyquist rate sampling. [PYQ: 2018, 2016, 2015] (Note 1.05)
• Draw the block diagram of the analog-to-digital (ADC) conversion process. [PYQ: 2023]
• Distinguish between Ideal, Natural, and Flat-top sampling techniques. [PYQ: 2017] (Note 1.05)
• Draw the criteria and frequency spectrum graphs for over-sampling, under-sampling, and Nyquist rate sampling. [PYQ: 2018, 2016, 2015] [Heavily Tested] (Note 1.05)
• Draw the specifications for an analog low pass filter with its tolerance curve. [PYQ: 2024]
• Calculate the compressed (down-sampled) and expanded (up-sampled) arrays from an input signal sequence. [PYQ: 2024, 2022] (Note 1.02)
• Design a Butterworth analog low pass filter (calculate order and transfer function) given passband ripple, stopband ripple, and edge frequencies. [PYQ: 2025, 2023]
• Design an Elliptic low pass filter (calculate order, ripple factor, and transfer function) given specific frequencies and attenuation decibels. [PYQ: 2025]
• Calculate the impulse response $h(n)$ of a low pass filter. [PYQ: 2024]
• Calculate the output response $y(t)$ of a low-pass RC network for an exponential input signal $x(t)=e^{-t/RC}$ using time-domain convolution. [PYQ: 2021, 2017, 2016, 2015] [Heavily Tested]

6. Network Theory (Two-Port Networks)

• Define “Network Theory”. [PYQ: 2025, 2022]
• Define what a “two-port network” is. [PYQ: 2024]
• Classify the types of parameters used in two-port networks. [PYQ: 2025, 2022]
• Calculate the ABCD (transmission) matrix parameters for a given T or Pi resistor network. [PYQ: 2025, 2024, 2022] [Heavily Tested]
• Calculate the Y (admittance) parameters for a given Pi-network. [PYQ: 2025, 2022]
• Calculate the Z (impedance) parameters for a given T-network. [PYQ: 2022]

Sources: Syllabus pg 1 (Instructor 2 scope), Notes (Rabiul sir -2309008.pdf, ECE-2107_STATE_SPACE_ANALYSIS.pdf, 04 Network Theory.pdf), PYQ 2015-2025.

missed:

Here are the exact missed items, categorized by chapter, formulated as action-based checklist items.

Chapter: Fourier Transform (Continuous Time)

Examiners love pulling properties directly from the lecture sheets that aren’t explicitly named in the main syllabus.

• Derive the Fourier Transform of a Rectangular Pulse (Gate Function) and sketch its amplitude (sinc function) and phase spectrum,. [Notes]
• Derive the Fourier Transform of a Unit Impulse/Dirac Delta function ($\delta (t)$) and prove it transforms to a constant. [Notes]
• State Rayleigh’s Energy Theorem and distinguish it from Parseval’s theorem for aperiodic signals. [Notes]
• Prove the “Area under $f(t)$” property (i.e., $\int f(t)dt=F(0)$) and the “Area under $F(f)$” property. [Notes]
• Apply the Duality Property of Fourier Transform to find the transform of a sinc function given the transform of a rectangular pulse. [Notes]

Chapter: Laplace Transform & Applications

Students usually master partial fractions but fail when asked to model initial conditions mathematically or interpret stability boundaries.

• Formulate the s-domain equivalent circuit models for Inductors and Capacitors, specifically accounting for initial conditions $i(0^{-})$ and $v(0^{-})$ using series voltage sources or parallel current sources. [Notes]
• Calculate the Laplace transform of composite functions using combined properties (e.g., $t\sin (\omega t)$ using frequency differentiation, or ${\cos }^3(3t)$ using trigonometric identities). [Notes]
• Differentiate between absolute stability, marginal stability (poles exactly on the $j\omega$-axis with no multiplicity), and instability using pole locations on the s-plane. [Notes]
• Explain the Routh-Hurwitz stability criterion as an analytical procedure for finding the range of a parameter for stability without explicitly solving higher-order denominator polynomials. [Notes]

Chapter: Z-Transform & Discrete Analysis

You will lose marks if you only know partial fractions for inverse Z-transforms. The examiner specifically asks for other methods.

• Calculate the inverse z-transform using the Long Division Method (Power Series Expansion) for specific ROCs (e.g., $|z|>1$ for causal, $|z|<1/3$ for anti-causal). [PYQ: 2017]
• Calculate the inverse z-transform using Cauchy’s Residue Theorem and apply the contour integration formula. [PYQ: 2019]
• Calculate the convolution of two sequences by multiplying their Z-transforms ($Y(z)=X(z)H(z)$) and taking the inverse Z-transform, rather than using tabular time-domain convolution. [Notes]

Chapter: Fast Fourier Transform (FFT)

The numericals were listed, but the internal architectural details of the algorithm were missed.

• Draw the complete 8-point butterfly diagram for both Radix-2 DIT-FFT and DIF-FFT algorithms, clearly labeling the phase factors ($W_N^k$),. [Notes]
• Explain the “bit-reversal” sorting process for inputs in DIT-FFT and outputs in DIF-FFT. [Notes]

Chapter: Discrete-Time Systems & Difference Equations

Reverse-engineering a system is a common trap.

• Formulate the specific Difference Equation mathematically by reverse-engineering a given discrete-time Block Diagram (e.g., identifying unit delays $z^{-1}$ and multiplier coefficients). [PYQ: 2021]
• Distinguish between Non-Recursive (FIR) difference equations and Recursive (IIR) difference equations in characterizing discrete-time systems. [PYQ: 2023]

Chapter: Network Theory & Filters

The main checklist captured Z, Y, and ABCD parameters, but the lecture notes contain more.

• Calculate the h-parameters (hybrid) and g-parameters (inverse hybrid) for a given two-port network. [Notes]
• Compare the frequency response characteristics (passband/stopband ripples, transition band steepness) of Butterworth, Chebyshev (Type I & II), and Elliptic filters,. [Book]

Chapter: MATLAB / Laboratory Implementation (ECE 2108)

A+ students don’t ignore the lab syllabus. ECE 2108 is directly tied to ECE 2107 theory. You must be able to code these concepts.

• Write MATLAB code to generate and plot standard signals (unit impulse, step, ramp, exponential, and noisy double frequency sine wave),. [Lab Syllabus]
• Write MATLAB code to compute the linear convolution of two given sequences $x(n)$ and $h(n)$ without using built-in convolution functions. [Lab Syllabus]
• Write MATLAB code to find the cross-correlation between sine, cosine, and square waves. [Lab Syllabus]
• Write MATLAB code to find the impulse response and step response of a system represented by a given differential equation. [Lab Syllabus]
• Write MATLAB code to extract poles and zeros and plot the pole-zero map (pzmap) to determine the stability of a system from its Laplace or Z-transform. [Lab Syllabus]