RTU Kota BTech 3rd Semester Signals and Systems Question Paper 2022 (ECE and BI)

RTU Signals and Systems 2022 Paper Review

Preparing for the Rajasthan Technical University BTech Signals and Systems exam requires a firm grasp of mathematical modeling, basic signal transformations, and continuous-domain analysis. For Electronics and Communication or Biomedical Engineering students designing analog filters, processing electrocardiogram (ECG) data, or analyzing RF transmission channels, mastering these mathematical proofs is foundational. You cannot build reliable medical diagnostic systems or telecommunication networks without understanding how signals compress, shift, and respond in the frequency domain.

The 2022 paper tests your capability to apply time-scaling and time-shifting operations, compute continuous-time Fourier series coefficients, and evaluate system stability using Laplace transforms. Publishing this specific 3rd-semester paper review directly to exam-support.in provides your users exactly what they need to structure their study plans around high-weightage calculus problems. This targeted preparation strategy helps approach the exam confidently, Aryan.

Understanding the Exam Pattern

The RTU theory examination is a three-hour paper worth 70 marks. The paper features three distinct sections designed to evaluate both theoretical definitions and complex mathematical derivations.

Part A: This section contains ten compulsory questions worth two marks each. You must define terms like orthogonal signals, state the time-shifting property of the Fourier transform, define the region of convergence (ROC), or explain the concept of an even and odd signal under 30 words.

Part B: You will find seven questions here. You must answer five of them. Each question is worth four marks. Your answers require sketching a transformed continuous-time signal, determining whether a given system is time-variant or time-invariant, or finding the Laplace transform of a basic exponential decay sequence.

Part C: This section offers five major questions. You need to answer three. Each question carries ten marks. These require you to calculate the trigonometric Fourier series of a full-wave rectified sine wave, perform graphical convolution for two rectangular pulses, or determine the overall transfer function and stability of a system described by a second-order linear differential equation.

Core Topics Evaluated in the Paper

The 2022 question paper covers critical modules that establish the mathematical rules for continuous signal analysis. Focus your study time on these specific areas to maximize your score.

Basic Signal Operations and Classification

This module evaluates your ability to manipulate signals graphically and mathematically. You must master the order of operations when a signal undergoes combined time-shifting and time-scaling. Practice sketching $y(t) = x(at - b)$ accurately. You must also evaluate system properties by testing equations for linearity and causality.

Continuous-Time Fourier Series (CTFS)

Periodic signals can be represented as infinite sums of harmonic sine and cosine waves. You must know how to calculate the DC component ($a_0$) and the harmonic coefficients ($a_n$ and $b_n$). Practice applying waveform symmetry conditions (even, odd, half-wave symmetry) to instantly determine which coefficients evaluate to zero, saving you massive amounts of integration time during the exam.

Fourier Transform and Signal Spectra

This module transitions aperiodic signals into the frequency domain. You must memorize standard continuous-time Fourier transform (CTFT) pairs and their properties. The 2022 exam heavily tested the duality property and Parseval's theorem, which requires you to relate the total energy of a signal in the time domain to its energy spectral density in the frequency domain.

Laplace Transforms and LTI Systems

Transforms convert complex differential calculus into straightforward algebra. Study the ROC properties extensively for right-sided and left-sided signals. The paper features long questions requiring you to determine the system transfer function $H(s)$, execute partial fraction expansions, and map the poles and zeros on the s-plane. You must state the mathematical definition of the continuous-time transfer function explicitly:

$$H(s) = \int_{-\infty}^{\infty} h(t) e^{-st} dt$$

Answer Writing Strategy for High Marks

RTU evaluators look for step-by-step mathematical derivations, explicitly stated transform properties, and clearly labeled signal plots. Use a blue pen for text explanations, equations, and calculus steps. Use a black pen and ruler for drawing signal waveforms, block diagrams, and s-plane plots.

In Part A, answer directly. If a question asks for the condition of a bounded-input bounded-output (BIBO) stable continuous-time LTI system, state clearly that the impulse response must be absolutely integrable.

In Part B, show your graphical operations explicitly. When asked to sketch $x(2t - 3)$, draw intermediate graphs showing the time-shift to $x(t - 3)$ first, followed by the time-compression to arrive at the final answer. Label the time axis coordinates at every step.

In Part C, mathematical precision is critical. When solving a ten-mark Laplace transform problem, state the specific ROC provided in the question, apply the Heaviside cover-up method for partial fractions cleanly, and select the correct inverse transform pair for each term before writing the final time-domain response $y(t)$.

Time Management During the Exam

Allocate exactly 20 minutes to Part A. Spend 40 minutes addressing the five short-answer questions in Part B. Reserve the remaining 120 minutes for the three long-answer questions in Part C. Evaluating definite integrals, executing algebraic partial fractions, and plotting precise waveforms requires steady focus and significant writing time. This distribution guarantees you 40 minutes per major question, giving you time to double-check your algebraic factoring. Use the final 10 minutes to verify your question numbering, ensure all integration limits are correct, and check that your s-plane shading matches the causality of the given system.