Video Lectures
 Topic Notes Lecture videos Video solutions to practice problems Python notebooks Chapter 1 - Math Review Notes in pdf Trigonometric Identities - read the notes Practice problems Complex Numbers (pdf) Complex Numbers - Cartesian and Polar forms Practice problems in Complex Numbers with video solutions Introduction to Complex Numbers.ipynb Practice problems Geometric Series (pdf) Example of Cartesian to Polar conversion Euler's formula Periodicity $e^{j \theta} = e^{j \theta + k 2 \pi}$, for any integer $k$ Polar representations of commonly used complex numbers Arithmetic operations with complex numbers Geometric interpretation of arithmetic operations Conjugate of a complex number nth power of complex numbers Cube roots of 1 How to find the $n$th roots of a complex number? nth roots of a complex number.ipynb Example for finding the $n$th root - 5th roots of $2e^{j\pi/5}$ Complex functions of a real variable, plotting their magnitude and phase Complex exponentials Complex exponentials.ipynb Simplifying complex numbers of the form $e^{j\theta_1}+e^{j\theta_2}$ Why are complex numbers useful? Integrals of complex functions of a real variable - Example 1 Integrals of complex functions.ipynb Integrals of complex functions of a real variable - Example 2 Integrals of complex functions of a real variable - Example 3 Brief history of complex numbers Roots of polynomials with real coefficients occur in conjugate pairs Geometric sequence intro, formula for partial sums Practice problems in Geometric Series with video solutions Geometricseries.ipynb Example for sum to $n$ terms of a geometric series Chapter 2 - Signals and Systems Chapter 2.1 - Signals Introduction What is a signal? (12 mins) Intro to Signals.ipynb What is a continuous-time signal and what is a discrete-time signal? (10 mins) Some ways to describe (or specify) a signal (10 mins) Energy and power Signal energy and Power - Part 1 (15 mins) Signal energy and Power Part 2 - Examples (30 mins) Basic operations Transformation of the dependent variable (recorded in class on 09/06/17 Scaling of the time axis (recorded in class on 09/06/17 Practice problems (combinations of shifting and scaling), Example (33 mins) Transformation of signals defined piecewise Transformations of signals defined piecewise Even and odd signals Even and Odd Signals - Definition, Even and odd Signals - properties, Conjugate symmetry for complex signals - Note: there is a small mistake at 2.08. The correct expression is $-x(t) = x^*(-t)$ Commonly encountered signals Description of Commonly Used Signals - Real exponentials, CT and DT Sinusoids Problems Description of Commonly used signals - complex exponentials Description of Commonly used signals - unit step, ramp, rectangular functions Description of Commonly used signals - discrete time impuse (Kronecker-delta) function Description of Commonly used signals - continuous time impulse (Dirac-delta) function Chapter 2.2 - Systems What is a system? What is a system ? - definition and examples System Properties What is a system with memory, examples What is a stable system, examples What is a Linear system - part1,part2 Definition of Time invariance Time invariance Examples Time invariance Example OWY127d Definition of Causality Why do we care about non-causal systems? Chapter 3 - Time Domain Analysis of Impulse response and Convolution Impulse response, definition of convolution (18mins) Linear Time Invariant Systems Computing impulse response Example - computing the impulse response(8 mins) DTconvolution procedure DTconvolution Computing the intermediate signal in Discrete Time Convolution - Warm up (19 mins) Discrete Time Convolution - Example 1 (15 mins) DT convolution using MATLAB Discrete Time Convolution - Example 2 (9 mins) Deriving the convolution integral Continuous Time Convolution - Example 1 (35 mins) CT convolution using MATLAB Continuous Time Convolution - Example 2 (15 mins) CT convolution Continuous Time Convolution - Example 3 (21 mins) Properties of LTI systems Properties of LTI systems - Memory and Causality Properties of LTI systems - Stability Properties of LTI systems - Invertibility Step response of an LTI system Response of an LTI system to a complex exponential Correlation between signals How echo location works [[Detection of gravity waves]] Correlation and Convolution Matched filter Chapter 4 - Frequency Domain Analysis of Introduction to Fourier Series Linear Time-Invariant Systems Computing FS Coeffs Computing FS coefficients - direct method Computing FS coefficients direct method - Example Computing FS coefficients by inspection, Example Relationship between the exponential, trig and polar forms of the FS [ Parseval's identity] Basel problem and Parseval's identity CTFS CTFS Synthesizer Matlab Project Continuous-time Fourier Transform Fourier Transform Introduction to Fourier transform FT of exponential signal FT of two sided exponential FT of the impulse function FT of a rectangular signal FT of a sinc signal or Inverse FT of a rectangular signal FT of constant signal $x(t)=1$ or Inverse FT of an impulse $X(j \omega) = 2 \pi \delta(\omega)$ FT of $x(t)=e^{j \omega_o t}$ or Inverse FT of $X(j \omega) = 2 \pi \delta(\omega-\omega_0)$ Properties of the Fourier Transform Linearity, Example Shift in time, Example Shift in Frequency Modulation property How radio stations transmit without interfering with each other Scaling in time, Why fast forwarding music makes it sound shriller Time reversal Conjugation and Symmetry Convolution-Multiplication Duality Convolution-Multiplication duality Multiplication in time and windowing Derivative & Integral Properties Derivative & Integral Properties Area under the curve property Duality FT of periodic signals FT of periodic signals Amplitude Modulation Amplitude Modulation AM Radio Matlab Project Filtering Low pass, high pass, band-pass and band-reject filters Interference Rejection in Wireless Communications Inverse FT of rational functions Where do we encounter rational functions for $X(j \omega)$ Inverse FT using partial fractions Sampling Fourier transform of impulse train, multiplication/conv property What is a bandlimited signal? Sampling Theorem, How to reconstruct a CT signals from samples Discrete-time processing of Continuous Time Signals 1 Chapter 6 - Laplace Transforms Laplace transform - review of complex exponentials, definition of the Laplace transform The signal plotted at 2 mins in the video is the real part of the signal, not the signal itself. Note that the signal is complex and hence cannot be plotted directly on paper Region of convergence Example for computing Laplace transform and ROC Another example, Poles and zeros Unilateral Laplace transform Properties of the unilateral Laplace transform Flipped Classroom Flipped classroom and its benefits
page revision: 360, last edited: 03 Oct 2021 16:25