# 1.3 Common continuous time signals

 Page 1 / 1
Presents several useful continuous time signals.

## Introduction

Before looking at this module, hopefully you have an idea of what a signal is and what basic classifications and properties a signal canhave. In review, a signal is a function defined with respect to an independent variable. This variable is often timebut could represent any number of things. Mathematically, continuous time analogsignals have continuous independent and dependent variables. This module will describe some useful continuous time analog signals.

## Sinusoids

One of the most important elemental signal that you will deal with is the real-valued sinusoid. In its continuous-timeform, we write the general expression as

$A\cos (\omega t+\phi )$
where $A$ is the amplitude, $\omega$ is the frequency, and $\phi$ is the phase. Thus, the period of the sinusoid is
$T=\frac{2\pi }{\omega }$

## Complex exponentials

As important as the general sinusoid, the complex exponential function will become a critical part of your study of signals and systems. Its general continuous form iswritten as

$Ae^{st}$
where $s=\sigma +j\omega$ is a complex number in terms of $\sigma$ , the attenuation constant, and $\omega$ the angular frequency.

## Unit impulses

The unit impulse function, also known asthe Dirac delta function, is a signal that has infinite height andinfinitesimal width. However, because of the way it is defined, it integrates to one. While this signal is useful for theunderstanding of many concepts, a formal understanding of its definition more involved. The unit impulse is commonly denoted $\delta (t)$ .

More detail is provided in the section on the continuous time impulse function. For now, it suffices to say that this signal is crucially important in the study of continuous signals, as it allows the sifting property to be used in signal representation and signal decomposition.

## Unit step

Another very basic signal is the unit-step function that is defined as

$u(t)=\begin{cases}0 & \text{if t< 0}\\ 1 & \text{if t\ge 0}\end{cases}$

The step function is a useful tool for testing and for defining other signals. For example, whendifferent shifted versions of the step function are multiplied by other signals, one can select a certain portion of thesignal and zero out the rest.

## Common continuous time signals summary

Some of the most important and most frequently encountered signals have been discussed in this module. There are, of course, many other signals of significant consequence not discussed here. As you will see later, many of the other more complicated signals will be studied in terms of those listed here. Especially take note of the complex exponentials and unit impulse functions, which will be the key focus of several topics included in this course.

I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!