Signals and systems
Module 00 - Course introduction
Introduction.
Module 02 - Time Transformations, Complex Exponentials
Learn basic transformations and signal properties by analyzing the role of the independent variable in discrete and continuous time. Also, review complex numbers and the relationship between exponentials and sinusoids in discrete and continuous time.
Module 03 - The Impulse, Step and System Properties
This module covers the discrete- and continuous-time impulse and step functions, two functions that are integral to the study of signals and systems. This module is also an introduction to systems and their mathematical properties.
module 04 - more system properties: linearity and time-invariance
Learn the two most important properties to the study of signals and systems: linearity and time-invariance.
module 05 - convolution
Given only how the LTI system responds to an impulse, one can find the output of the system due to any input using the mathematical operation known as convolution. Learn discrete- and continuous-time convolution in this module.
module 06 - LTI systems and convolution, difference and differential equations
Don't get caught up in the math! Always keep an engineering perspective! This module covers the application of convolution in engineering and also how difference and differential equations can be used to describe causal discrete- and continuous-time LTI systems.
Module 07 - The Continuous-Time Fourier series
This module begins the second half of the material: The analysis of signals and systems in frequency instead of time. The ability to characterize signals and systems in terms of frequency has far-reaching consequences and applications including medical imaging, mp3 compression, and wireless communication.
module 08 - properties of the continuous-time fourier series, programming the synthesis
Properties of the Fourier series allow for the speedy calculation of the Fourier series for more complicated signals. These properties also provide insight into how adjustments in time affect the frequency content of the signals. Also covered in this module is how to program the Fourier series synthesis, reconstructing a periodic signal by adding its individual frequency components together.
Module 09 - The Discrete-time fourier series and its properties
Similar to its continuous-time counterpart, the discrete-time Fourier series characterizes the frequency of periodic signals, but in discrete time.
Module 10 - Fourier series and lti systems
Studying how the Fourier series coefficients of a signal are affected as a signal passes through LTI systems allows us to understand how the systems shape frequency bands. This, in turn, allows for designs and applications never possible by time-based analysis alone.
Module 11 - The continuous-time Fourier transform
The Fourier transform does everything the Fourier series does but for both periodic and aperiodic signals, making it more applicable than the Fourier series.
module 12 - properties of continuous-time fourier transform, frequency response and differential equations
Properties of the continuous-time Fourier transform allow for the rapid calculation of Fourier transforms of more complicated signals, as well as provide insight as to how time adjustments affect signal frequency content. Differential equations can be used to model the behavior of causal LTI systems, from which we can deduce a frequency response.
module 13 - The Discrete-Time fourier Transform
The discrete-time Fourier transform does everything the Fourier series does but for periodic and aperiodic signals, making it more applicable than the Fourier series.
module 14 - properties of the Discrete-Time fourier transform
Properties of the discrete-time Fourier transform allow for the rapid calculation of the Fourier transform of more complicated signals, as well as provide insight into how time adjustments affect signal frequency content.
module 15 - frequency response and difference equations
Difference equations can be sued to model the behavior of causal discrete-time LTI systems, from which we can deduce a frequency response.
