Signal Operations: Combined Operations

Signal Operations: Time Shifting

Signal Operations: Time Reversal

Signal Operations: Time Scaling

Signal Operations on Dependent Variables

Signals and Systems Definitions

Continuous-Time Deterministic and Random Signals

Simply-Defined and Piecewise-Defined Signals

Sums of Periodic Signals Example

Continuous-Time Periodic and Non-Periodic Signals

Even and Odd Signal Properties With Proofs

Continuous-Time Conjugate Symmetric Signals

Continuous-Time Even and Odd Signals

Analog and Digital Signal Definitions

Continuous-Time vs. Discrete-Time Signals

Orthogonal Projection of Vectors

Representing Vectors with an Orthogonal Basis

Orthogonal Sets of Vectors

Orthogonal Complements

Finding Orthogonal Vectors in R3

Finding Orthogonal Vectors in R2

The Parallelogram Law

Dot Product and Norm Examples

Definition of Orthogonal Vectors

The Distance Between Two Vectors

The Norm of a Vector

Dot Product Properties (with proofs)

Inner Product Introduction

Block Decoding Minimum Distance Decoding Rule Derivation

The Hamming Distance

Block Coding Introduction

Shannon's Capacity Formula

Channel Capacity and the Channel Error Exponent

Information Theory and Error Control Coding Overview

Digital Communication Symbol Synchronization (Early/Late Gate)

Digital Communication Costas Loop for BPSK

Digital Communication Binary Phase Shift Keying (BPSK) Squaring Loop

Digital Communication Phase Lock Loop (PLL) Analysis

Digital Communication Carrier Synchronization Introduction

9.6 The Quadratic Formula: Discriminant and Number of Solutions

9.6 The Quadratic Formula: Appropriate Solutions

9.6 The Quadratic Formula: Solving Equations

9.5 Completing the Square: When a is not 1

9.5 Completing the Square: The Vertex Of A Parabola

9.5 Completing the Square: Perfect Square Trinomials

9.5 Completing the Square: When a = 1

Matlab System Frequency Response from Pole/Zero Plots

Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) Filters

A Time-Domain Digital Filter Design Criteria

A Frequency-Domain Digital Filter Design Criteria

Finding the System Frequency Response from Pole/Zero Plots

System Frequency Response Examples

Channel Update 11/17/19

Computing the System Frequency Response from Difference Equation

Introduction to Digital Filter Design

Unilateral Z-Transform Difference Equation Solution #2

Graphical Derivation of System Amplitude Response

Finding the Difference Equation from the System Transfer Function

The Transfer Function of a Discrete-Time Linear System

The Inverse Z-Transform by Long Division Example #2