Shreyaakulkarni

Signals & Systems Units I–V concise notes covering essentials for exams. Unit I: signal types & system properties. Unit II: signal operations & convolution. Unit III: Fourier Series & Transform. Unit IV: Laplace Transform. Unit V: Z-Transform. Formula-focused, exam-ready, ideal for quick revision.

These notes provide a concise class notes of Unit III: Fourier Analysis of Signals. The content covers Fourier Series for periodic signals and Fourier Transform for aperiodic signals, including the definitions, formulas, and properties. Key properties such as linearity, time shifting, frequency shifting, and convolution are summarized for quick understanding. The notes focus on frequency-domain representation of signals and are exam-oriented, making them suitable for quick revision and proble...

These notes provide a concise class notes of Unit I: Fundamentals of Signals and Systems. The content introduces basic signal concepts and classifications, including continuous-time and discrete-time signals, even and odd signals, periodic and aperiodic signals, and energy and power signals. Common elementary signals such as unit step, impulse, ramp, and exponential signals are explained. The notes also summarize system properties including linearity, time invariance, causality, stability, an...

These notes provide a concise class notes of Unit II: Operations on Signals and System Representations in Signals and Systems. The content includes signal operations such as time shifting, time scaling, and reversal, as well as signal addition and multiplication. It also covers convolution in both continuous-time and discrete-time signals, explaining its role in analyzing linear time-invariant (LTI) systems. The notes are formula-focused and exam-oriented, making them ideal for quick revision...

These notes provide a concise class notes of Unit IV and Unit V of Signals and Systems, focusing on transform-domain analysis of signals and systems. Unit IV covers the Laplace Transform, including its definition, conditions of existence, region of convergence (ROC), and important properties. The notes summarize methods for finding the inverse Laplace transform and highlight applications of Laplace transform in continuous-time LTI system analysis, including stability and system behavior. U...

These notes present a concise summary of Unit II: Random Variables from Probability Theory. The content introduces discrete and continuous random variables, along with the distribution function (CDF) and its properties. Key probability relations and methods for finding probabilities using CDF, PMF, and PDF are included. The notes summarize mathematical expectation, moments about origin and mean, variance, and standard deviation, with essential formulas. The concept of the Moment Generating Fu...

These notes provide a concise summary of key concepts in Probability Theory, focusing specifically on Unit II and Unit III topics. Unit II covers the fundamentals of random variables, including discrete and continuous random variables, moments, moment generating functions, cumulative distribution functions, and brief derivations of standard distributions such as Binomial, Poisson, Uniform, Exponential, and Normal distributions, along with functions of a random variable . Unit III introduces two...