| An Introduction To Signals |
An Introduction To Signals
Why
Do You Need To Know About Signals?
Electricity has been with us for a while now, and we use it in many ways
that were never anticipated when we began to use electricity.
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After electricity was
discovered and understood, almost all of the first applications were ones
that involved power. The application may have been an electric light
or it may have been a motor. In either case, the application of electricity
involved the use of large amounts of energy and power.
-
However, other early applications
of electricity were used to transmit information. The telegraph,
and later the telephone, had a very significant effect on the history of
the United States.
-
As things progressed it
became necessary to design an build systems to distribute large amounts
of electrical power.
-
The city of Sunbury, PA,
was the first to have an electrical distribution system for lighting on
July 4, 1883. That system was a DC system.
-
Later, AC systems were
developed. Edison, who installed that first DC system in Sunbury,
and who had begun installing DC systems in many other cities bitterly fought
the introduction of AC systems. Edison put out advertisements that
showed an electric chair and asked the public if they wanted AC in their
home since it was used in the electric chair for killing people.
AC
systems prevailed, despite Edison's protestations. AC systems were
based on a time varying voltage. (AC stands for Alternating Current.)
As people learned to deal with these time varying voltages they realized
that time varying voltages could be used to transmit information.
With the invention of radio it was realized that information could be transmitted
by controlling the parameters of a sinusoidally varying voltage.
Today, we have vast industries that use electricity to distritute information.
Those industries are the TV networks (over the air, cable and satellite),
phone systems, the internet and other radio communciation systems, for
example.
If you want to understand the basics of how the information distribution
industry works you will need to know about the various forms of electrical
signals.
Goals
For This Lesson
Goals for this lesson are simple.
Given a signal,
Be able to describe the signal when possible.
Be able to use time-varying currents and voltages in KCL and KVL.
Electrical
Signals
There are many different kinds of electrical signals. If we look
at how signals are generated, we find that there are many different kinds
of electrical signal sources. Here are some.
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Microphones
-
Fax machines
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Thermocouples
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Remote controls for television
sets
What
could possibly all of these signals have in common? Well, they are
all electrically generated signals, and electrical engineers have to deal
with them.
-
If you are a sound engineer, you will have to
deal with the small voltages produced by microphones and you will have
to worry about processing the signal so that you can reproduce the sound
signals accurately.
-
If you design fax machines you will need to
ensure that your signals are transmitted accurately so that information
is not corrupted when it is sent.
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If you need to control temperature in an industrial
process, you will need to worry about the small signal from a thermocouple
- how to amplify it - how to process it.
-
TV remotes are designed to set the channel accurately.
They set the channel, adjust volume, etc. by sending signals to the TV.
What
is common through all of this is the need to be able to manipulate signals
in different ways. That might include doing one or more of the following.
-
Amplify a signal - make
it larger
-
Remove noise from a signal
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Change a signal to emphasize
certain characteristics - for example adding bass boost to a sound signal.
When you start to operate on signals in this
way you are entering the realm of signal processing. Today, signal
processing is often done after digitizing a signal - making a digital version
of the signal - and the processing that is done there is referred to as
digital signal processing, or simply DSP.
If you will be dealing with signals, then you will need to have some sort
of model for the signals you work with. Usually that will be some
sort of mathematical representation.
The simplest representation for a signal is to represent the signal as
a function of time. For example, the voltage that appears across
the terminals of a microphone will vary in time when the microphone "picks
up" a sound. Then, we might say something like:
Microphone voltage
= Vmike(t)
Representing a signal as a time function
is so common that there are many instruments and data gathering devices
that give you a picture of a voltage time function. The most common
instrument that gives a picture of a voltage time function is the oscilloscope.
At this point, we can consider some specific kinds of signals. We'll
start with periodic signals, and in particular we'll start with sinusoidal
signals.
Periodic
Signals
Periodic signals are signals that repeat in time with a certain period.
The most fundamental periodic signal is the sinusoidal signal. Any
other periodic signal can be thought of as a combination of sinusoidal
signals added together. That approach is based on the Fourier Series
and you can go to that topic when you know enough about sinusoidal signals.
In this section you will begin to learn about sinusoidal signals.
Sinusoidal signals, based on sine and cosine functions, are the most important
signals you will deal with. They are important because virtually
every other signal can be thought of as being composed of many different
sine and cosine signals. They form the basis for many other things
you will do in signal processing and information transmission. Eventually
you will deal with signals as different as voice signals, radar signals,
measurement signals and entertainment signals like those found in television
and radio. Sinusoidal signals are the starting point for almost all
work in signal processing and information transmission.
In this part of this lesson you will learn:
-
What Sinusoidal Signals
are and How they are Represented
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The Parameters of a Sinusoidal
Signal
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How to Measure the Parameters
of a Sinusoidal Signal.
Representation
of Sinusoidal Signals
If you put a voltage signal into an oscilloscope you can get a picture
of how the signal varies in time. Sinusoidal signals are often voltages
which vary sinusoidally in time. (Sinusoidal signals could be, however,
other physical variables like current, pressure, or virtually any other
physical variable.) Here's a simulator that will let you put various
kinds of signals on a simulated oscilloscope. Click the Start
button to see a typical sinusoidal signal.
You can write a mathematical expression for
the voltage signal as a function of time. Call that mathematical
expression V(t). V(t) will have this general form.
V(t) = Vmaxsin(wt
+ f)
This signal has three parameters, the maximum
voltage, or amplitude, denoted by Vmax, the angular frequency
denoted by w
and the phase angle denoted by f.
We'll examine these separately.
Amplitude
of Sinusoidal Signals
The amplitude of a sinusoidal signal is the largest value it takes (when
the sine function has a value of +1 or -1). Amplitude has whatever
units the physical quantity has, so if it is a voltage signal, like the
one below, it might have an amplitude of 10 volts. On the other hand
if the shock absorbers on your car are bad, your car can run down the road
and vibrate up and down with an amplitude of three inches. For the
signal we saw above - repeated here - the amplitude is 100 volts.
However, you can change the amplitude of the sinusoidal signal here by
typing in a different value. Do that now.
Problem
P1.
Here is a sinusoidal signal. Willy Nilly has measured this signal,
and acquired it in a computer file and plotted it for you. Determine
the amplitude of this signal.
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