Signals and Systems

This page is under construction. For now, you can find all of the signals and systems videos at https://sites.google.com/a/asu.edu/signals-and-systems/

Contents

1 Introduction to Signals and Systems
2 Continuous-time Signals
3 Discrete-time Signals
4 Discrete-time Systems
5 Continuous-time Convolution
6 Discrete-time Convolution
7 Laplace Transform
8 Fourier Analysis

Introduction to Signals and Systems

Signals and Systems Introduction This video provides a basic introduction to the concept of a system and signals.
Signals and Systems HVAC Example An example of how a heating or air conditioning system can be represented from the perspective of systems and signals.
Signals and Systems Cruise Control Example An example of considering the cruise control system of a car from the perspective of systems and signals.
System Properties: Stability and Causality An introduction to SISO/MIMO, stability, and causality as properties of a system.
System Properties: Linearity and Time Invariance An introduction to linearity and time invariance as properties of a system.
Introduction to Discrete-Time Signals and Systems A conceptual introduction to discrete-time signals and systems.

Continuous-time Signals

Unit Step Function and Delta Function Introduces the unit step function and delta function.

Integrals with Delta Functions How to work integrals that contain delta functions.

Signals: Sinusoids and Real Exponentials Introduces sinusoids and real exponentials.
Signals: Complex Exponentials Introduces complex exponentials.
Operations on Signals: Scaling and Addition Demonstrates scaling and addition of signals.

Discrete-time Signals

DT Signals-Unit Step and Delta Introduces the discrete-time unit step and delta functions.
DT Signals-Real Exponentials Introduces discrete-time real exponential signals.
DT Signals-Real Sinusoids Introduces discrete-time sinusoidal (sine and cosine) signals.
DT Signals-Complex Exponentials Introduces discrete-time complex exponential signals.
DT Signal Property-Periodic Introduces the definition of periodic for a discrete time signal and shows six examples of determining whether a signal is periodic, and if it is, determining its fundamental period.
DT Signal Property-Even and Odd Introduces the definitions of even and odd for a discrete time signal and shows seven examples of determining whether a signal is even, odd, or neither. Signals that are neither even nor odd are decomposed into their even and odd components.
DT Signal Property-Energy and Power Introduces the energy and average power for a discrete-time signal and shows four examples of computing energy and/or power.
DT Signals-Time Shifting and Reversal Shows how to time shift and reverse discrete-time signals.
Summing Geometric Series Shows how to sum a geometric series.

Discrete-time Systems

DT System Properties Example: y[n] = x[-n] Shows how to determine whether the system defined by the equation y[n] = x[-n] is 1) memoryless, 2) time invariant, 3) linear, 4) causal, and 5) stable.
DT System Properties Example: y[n] = nx[n] Shows how to determine whether the system defined by the equation y[n] = nx[n] is 1) memoryless, 2) time invariant, 3) linear, 4) causal, and 5) stable.
DT System Properties Example: y[n] = x[n] - x[n-1] Shows how to determine whether the system defined by the equation y[n] = x[n] - x[n-1] is 1) memoryless, 2) time invariant, 3) linear, 4) causal, and 5) stable.
DT System Properties Example: y[n] = x[n]x[n+1] Shows how to determine whether the system defined by the equation y[n] = x[n]x[n+1] is 1) memoryless, 2) time invariant, 3) linear, 4) causal, and 5) stable.

Continuous-time Convolution

Convolution Example: Unit Step with Exponential An example of computing the continuous time convolution of a unit step function with an exponential function.
Convolution Example-Two Rectangular Pulses An example of computing the continuous-time convolution of two rectangular pulses.

Discrete-time Convolution

DT LTI System Response: Convolution Shows how the response of a discrete-time LTI (Linear Time-Invariant) system to an arbitrary input is obtained as the convolution of the impulse response of the system with the input.
DT Convolution-Simple Example Shows how to compute the discrete-time convolution of two simple waveforms.
DT Convolution-Two Rectangular Pulses Shows how to compute the discrete-time convolution of two rectangular pulse waveforms.
DT Convolution-Two Exponentials Shows how to compute the discrete-time convolution of two exponential signals.

Laplace Transform

Laplace Transform Example-Unit Step Computing the Laplace transform of the unit step function using the integral definition of the Laplace transform.

Fourier Analysis

Fourier Analysis-Introduction Introduction to some applications and concepts associated with frequency domain (Fourier) analysis.

Fourier Series

Fourier Series Example-Square Wave Computing the complex exponential Fourier series coefficients for a square wave.
Fourier Series Example-Arbitrary Square Wave Computes the Fourier series coefficients of a square wave with arbitrary period T, amplitude A, and duty cycle D.
Fourier Series-Rectified Sine Wave Computes the Fourier series coefficients of a rectified sine wave; the computation is done entirely using Fourier series properties and Fourier series coefficients computed in previous videos. The DTFS properties used include multiplication, time shifting, linearity, and frequency shifting.

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.

Fourier Transform

Introduction to the Fourier Transform Introduces the mathematical definition of the Fourier transform as well as magnitude and phase spectra.
Fourier Transform Example-Rectangular Pulse Computing the Fourier transform of a rectangular pulse using integration.
AM Modulation and Demodulation This video uses properties of the Fourier transform to explain modulation and demodulation inside a simple AM radio system.

Discrete-time Fourier Transform

Introduction to the DT Fourier Transform Introduces the discrete-time Fourier Transform and shows two simple examples of computing the DT Fourier Transform.
DT Fourier Transform-Exponential Computes the discrete-time Fourier transform of an exponential signal.
DT Fourier Transform-Rectangular Pulse Computes the discrete-time Fourier transform of a rectangular pulse.
DT Fourier Transform-Ideal Filters Computes the impulse response of ideal low-pass and high-pass discrete-time filters using the frequency shifting property.
DT Fourier Transform-Triangle Wave Computes the discrete-time Fourier transform of a triangle wave using the convolution property.
DT Fourier Transform-Rectangular Window Computes the discrete-time Fourier transform of a cosine wave that has been windowed by a rectangular window. This is done using the multiplication property.
DT Fourier Transform-Filter Output Computes the output of a filter in response to a periodic square wave input by using the frequency response and the discrete-time Fourier transform. The relationship between DT Fourier series coefficients and DT Fourier transform is also used.

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