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.
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.
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.
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.
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.
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.
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.
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.
This lecture compares discrete-time and continuous-time sampling, and the differences between down-sampling (decimation) and up-sampling (reconstruction of original sequence).
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.
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.
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.
Discussion of complex exponential and sinusoidal modulation for discrete-time signals. Introduction and analysis of pulse carriers in continuous-time, sampling theorem.
This lecture covers mathematical representation of signals and systems, including transformation of variables and basic properties of common signals.
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.
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.
This video gives a summary of relationships between continuous-time and discrete-time Fourier series and Fourier transforms.
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.
This video lecture discusses continuous-time Fourier serires, and the response of continuous-time LTI systems to complex exponentials. Also covered: the eigenfunction property.
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.