This video covers the Laplace transform, in particular its relation to the Fourier transform.  We will see cover regions of convergence, poles and zeroes, and inverse transforms using partial fraction expansion.

Lecture 20, The Laplace Transform

In this lecture we wil continue our discussion of properties of the z-transform.  Covers systems characterized by linear constant-coefficient difference equations, and transformations between continuous-time and discrete-time systems.

Lecture 23, Mapping Continuous-Time Filters to Discrete-Time Filters

This lecture covers the z-Transform with linear time-invariant systems.  We will discuss the relationship to the discrete-time Fourier trasform, region of convergence (ROC), and geometric evaluation of the Fourier transform from the pole-zero plot.

Lecture 22, The z-Transform

This video covers the open loop system and explores choices for feedback dynamics. We will use proportional and derivative feedback to reach pendulum stability. Demonstration of an inverted pendulum on a track, and the effect of changing system dynamics.

Lecture 26, Feedback Example: The Inverted Pendulum

This lecture we cover Butterworth filters, including: parameters, cutoff frequency, filter order, and distribution of poles. Also covers the design of a discrete-time Butterwoth filter using impulse invariance, and also using the bilinear transformation.

Lecture 24, Butterworth Filters

In this lecture we will discuss feedback systems, applications and consequences. Feedback can cause destabilization, but also be used to stabilize unstable systems through inverse system design, compensation for nonideal elements, and root-locus analysis.

Lecture 25, Feedback

This lecture we will discuss sampling to reconstruct the output of a sinusoidal oscillator and the effect of undersampling: aliasing. This includes a visit to Doc Harold Edgerton's MIT Strobe Laboratory to demonstrate cases where aliasing can be useful.

Lecture 16, Sampling

Characteristics of second-order systems, geometric evaluation of frequency responses from pole-zero plots, system function for first-order and second-order systems. Overdamped and underdamped systems, a demonstration of these systems for speech synthesis.

Lecture 21, Continuous-Time Second-Order Systems	

This lecture compares discrete-time and continuous-time sampling, and the differences between down-sampling (decimation) and up-sampling (reconstruction of original sequence).

Lecture 19, Discrete-Time Sampling

In this lecture we will learn how to use sampling to convert continuous-time signals into discrete-time signals for processing.  We will also demonstrate how to reconstruct a signal by processing an impulse train with a low-pass filter.

Lecture 18, Discrete-Time Processing of Continuous-Time Signals

Signals and Systems: an Introduction to Analog and Digital Signal Processing, 1987

In this lecture we will see how linear interpolation is used to reconstruct a signal from its sample.  Reconstructing a signal by processing an impulse train with a low-pass filter.

Lecture 17, Interpolation

In this lecture we will cover continuous-time modulation: sinusoidal amplitude modulation, synchronous and asynchronous demodulation.  We will discuss communication applications, such as frequency-division multiplexing and single-side band modulation.

Lecture 13, Continuous-Time Modulation

Discussion of complex exponential and sinusoidal modulation for discrete-time signals.  Introduction and analysis of pulse carriers in continuous-time, sampling theorem.

Lecture 15, Discrete-Time Modulation

This lecture covers mathematical representation of signals and systems, including transformation of variables and basic properties of common signals.

Lecture 6, Systems Represented by Differential Equations

Lecture 14, Demonstration of Amplitude Modulation.  Demonstration with Professor Sandy Hill from the University of Massachusetts at Amherst. RC audio generator, oscilloscope, and spectrum analyzer demonstrations with speech and radio.

Lecture 14, Demonstration of Amplitude Modulation

Demonstration: a look at filtering in a commercial audio control room.  Covers many types of filters: selective filters, moving average filters, low-pass and high-pass filters, and commercial applications.

Lecture 12, Filtering

This video gives a summary of relationships between continuous-time and discrete-time Fourier series and Fourier transforms.

Lecture 11, Discrete-Time Fourier Transform

This lecture will discuss the similarities and differences with discrete-time and continuous-time Fourier series.  Analysis and synthesis equations, and approximation of periodic and aperiodic signals.

Lecture 10, Discrete-Time Fourier Series

This video lecture discusses continuous-time Fourier serires, and the response of continuous-time LTI systems to complex exponentials.  Also covered: the eigenfunction property.

Lecture 7, Continuous-Time Fourier Series

This video covers Fourier transofrm properties, including linearity, symmetry, time shifting, differentiation, and integration.  We will also cover convolution and modulation properties and how they can be used for filtering, modulation, and sampling.

Lecture 9, Fourier Transform Properties

The fundamentals are beautifully explained.

Very useful for beginners

This video covers the the unit step and impulse signals.  System properties are discussed, including memory, invertibility, causality, stability, and time invariance.

Lecture 3, Signals and Systems: Part II

This lecture video discusses representation of signals in terms of impulses.  Linear, time-invariant (LTI) systems, properties and representation.

Lecture 4, Convolution

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