Video Lectures
Topic Notes Individual pages, videos, etc Homework /Computer projects
Flipped Classroom Flipped classroom and its benefits
Chapter 0 - Math Review Notes in pdf Trigonometric Identities - read the notes
Complex Numbers - Cartesian and Polar forms
Euler's formula (7 mins), Proof of Euler's formula (6 mins)
$e^{j \pi}+1=0$ is called Euler's identity. It is a special case of Euler's formula and is considered to be the most beautiful theorem in mathematics
Conjugate of a complex number
Arithmetic operations with complex numbers
nth power and nth roots of complex numbers
Example for nth root - 5th roots of $2e^{j\pi/4}$
Complex functions of a real variable, plotting their magnitude and phase
Simplifying complex numbers of the form $e^{j\theta_1}+e^{j\theta_2}$
Why are complex numbers useful?
Geometric sequence intro, formula for partial sums
Example for sum to $n$ terms of a geometric series
Integrals of complex functions of a real variable
Chapter 1 - Signals and Systems
Chapter 1.1 - Signals Introduction What is a signal? (12 mins)
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 1.2 - 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 2 - 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 3 - 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
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
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