### Instructional Videos

These videos have been developed to support EGR 433: Transforms and Systems Modeling taught in the Engineering Department at the Polytechnic Campus of Arizona State University. Videos on engineering topics (currently circuit analysis and statics) are available at http://www.engineeringvideos.org.

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Video Topics

## System Properties

### System State

• System State Introduction Introduction to the concept of system state and how you might figure out what the state of a system is.

### Linearity

• Linearity Definition Explains how homogeneity and additivity, two attributes of a system, determine whether or not the system is linear.
• Linearity of a Gain Example An example of determining whether a gain (a system that scales the amplitude of a signal) is a linear system.
• Linearity of a Squarer Example An example of determining whether a system whose output is the square of its input is a linear system.
• Linearity and Time Invariance of an RC Circuit Example An example of determining whether an RC circuit is linear and time invariant. This provides some conceptual ideas about the role of initial conditions in systems whose dynamics are described by differential equations.

### System Response

• System Response Characterization How we characterize the response of a system to a unit step function input in terms of steady-state error, rise and fall time, overshoot, and settling time.

## LTI Systems and Convolution

### Continuous-time

• LTI Systems Introduction An explanation of how an LTI (Linear Time-Invariant) system is completely specified in terms of its impulse response, transfer function, or frequency response.
• Convolution and LTI Systems Shows how the response of an LTI system to an arbitrary input is obtained as the convolution of the impulse response of the system with the input.
• Convolution Properties A short explanation that convolution is commutative, associative, and distributive. In addition, an explanation of what happens when you convolve a signal with a delta function.
• Convolution Example: Unit Step with Exponential An example of computing the continuous time convolution of a unit step and an exponential signal.
• Convolution Example: Two Rectangular Pulses An example of computing the continuous-time convolution of two rectangular pulses.

## Fourier Analysis

### Discrete-time Fourier Series

• Introduction to DT Fourier Series Introduces the discrete-time Fourier Series (closely related to the DFT) and shows how to find the Fourier series coefficients of sampled cosine and sine waveforms.
• DT Fourier Series-Simple Example Computes the discrete-time Fourier series coefficients of a waveform with period N=8.
• DT Fourier Series-Periodic Square Wave Computes the discrete-time Fourier series coefficients of a square wave with period N and pulse width Np samples; the duty cycle is Np/N.
• DT Fourier Series-Rectified Sine Wave Computes the discrete-time Fourier series coefficients of a rectified sine wave; the computation is done entirely using DTFS properties and Fourier series coefficients computed in previous videos. The DTFS properties used include  multiplication, time shifting, linearity, and frequency shifting.
• DT Fourier Series-Periodic Triangle Wave Computes the discrete-time Fourier series coefficients of a triangle wave using the DTFS convolution property.

## Other Engineering Topics

Videos on circuit analysis and static mechanics are available at http://www.engineeringvideos.org/circuit-analysis.

## Acknowledgment

The idea for these videos came from the magnificent work of Salman Khan; in this case, imitation truly is the sincerest form of flattery.
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