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Richard Baraniuk - Signals and Systems

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Richard Baraniuk Signals and Systems

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This course deals with signals, systems, and transforms, from their theoretical mathematical foundations to practical implementation in circuits and computer algorithms. At the conclusion of ELEC 301, you should have a deep understanding of the mathematics and practical issues of signals in continuous and discrete time, linear time invariant systems, convolution, and Fourier transforms.

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Signals and Systems

Collection edited by: Richard Baraniuk

Content authors: Melissa Selik , Richard Baraniuk , Michael Haag , Stephen Kruzick , Don Johnson , Dan Calderon , Thanos Antoulas , John Slavinsky , Dante Soares , Justin Romberg , Ricardo Radaelli-Sanchez , Catherine Elder , Benjamin Fite , Roy Ha , C. Burrus , Steven Cox , and Matthew Hutchinson

Online:

This selection and arrangement of content as a collection is copyrighted by Richard Baraniuk .

It is licensed under the Creative Commons Attribution License: http://creativecommons.org/licenses/by/3.0/

Collection structure revised: 2011/10/11

For copyright and attribution information for the modules contained in this collection, see the "" section at the end of the collection.

Chapter 1. Introduction to Signals

1.1. Signal Classifications and Properties

Introduction

This module will begin our study of signals and systems by laying out some of the fundamentals of signalclassification. It is essentially an introduction to the important definitions andproperties that are fundamental to the discussion of signalsand systems, with a brief discussion of each.

Classifications of Signals
Continuous-Time vs. Discrete-Time

As the names suggest, this classification is determined by whether or not the time axis is discrete (countable) or continuous (, often created by sampling a continuous signal, will only have values at equally spaced intervals along the time axis.

Figure 1.1.

Analog vs Digital The difference between analog and digital is similar to the - photo 1

Analog vs. Digital

The difference between analog and digital is similar to the difference between continuous-time and discrete-time. However, in this case the difference involves the values of the function. Analog corresponds to a continuous set of possible function values, while digital corresponds to a discrete set of possible function values. An common example of a digital signal is a binary sequence, where the values of the function can only be one or zero.

Figure 1.2.

Periodic vs Aperiodic to be true Figure 13 a A periodic signal - photo 2

Periodic vs. Aperiodic

to be true.

Figure 1.3.

a A periodic signal with period T 0 b An aperiodic signal Finite - photo 3
(a) A periodic signal with period T 0
b An aperiodic signal Finite vs Infinite Length As the name implies - photo 4
(b) An aperiodic signal

Finite vs. Infinite Length

As the name implies, signals can be characterized as to whether they have a finite or infinite length set of values. Most finite length signals are used when dealing with discrete-time signals or a given sequence of values. Mathematically speaking, f ( t ) is a finite-length signal if it is nonzero over a finite interval t 1 < f ( t ) < t 2 where t 1 > and t 2 < . An example can be seen in . Similarly, an infinite-length signal, f ( t ) , is defined as nonzero over all real numbers: f ( t )

Figure 1.4.

Finite-Length Signal Note that it only has nonzero values on a set finite - photo 5
Finite-Length Signal. Note that it only has nonzero values on a set, finite interval.
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