The basic definition of bandwidth is that it is the width
of the spectrum that a signal occupies. The human ear can only hear sounds with
frequencies up to around 20kHz and this value reduces slowly as people grow
older. The bandwidth of a radio signal is generally related to the audio quality
for either analogue or digital radio systems but that is not the whole story
because bandwidth has very definitions for analogue bandwidth and digital
bandwidth. If you’re not interested in the definition of bandwidth then skip
the rest of this section but just remember that kbps means thousand bits per
second, and Mbps means million bits per second.
Because bandwidth is an often used word these days I think
it would be best to define what it is first because it crops up so often. The
term bandwidth is used for both analogue and digital systems and means similar
things but is used in very different ways. In a digital system it is used as an
alternative term to bit rate, which is the number of bits per second, usually
displayed as kilobits per second (kbps, kbit/s, or kb/s) or megabits per second
(Mbps, Mbit/s, or kb/s). Here kilo = thousand, and mega = million, so 2 kbps
equals 2,000 bits per second and so on. By the way, using ‘K’ means 1,024
bits, just to confuse things. This is the way approximately 1,000 is used in the
computing industry because it is equal to 2 to the power of 10 = 1024 and base 2
is the base used for digital because it can take on 2 values, just as decimal
numbers consist of 10 numbers, the numbers 0-9.
Analogue bandwidth is very different to this and more
complicated. In communications engineering a concept called Fourier Theory is
used to analyze signals as the sum of sinewaves with different frequencies. That
is, if you wanted to make a square wave signal (like a digital signal where
alternate ones and zeros are transmitted), you could add up a few sinewaves with
different frequencies and different amplitudes and if you added enough together
the resulting waveform would look like a square waveform. This can be applied in
the other direction so that a signal that you receive can be analysed as a bunch
of sinewaves at different frequencies with different amplitudes. The technique
that makes this possible is called the Fourier Transform, named after Joseph
Fourier who discovered these techniques. The modern way of analyzing a signal in
terms of its frequency components (sinewaves) is by using the Fast Fourier
Transform (FFT) which is a digital implementation of the Fourier Transform but
can be implemented extremely efficiently either in hardware or software.
Analogue bandwidth is measured in Hertz (Hz) which means
cycles per second. Signals are either periodic which means that they repeat
after a certain time duration and every period is the same as all previous
periods, or a signal is aperiodic or non-periodic (same thing) meaning that it
doesn’t repeat. Most real signals are aperiodic, and in fact periodic signals
carry no information apart from the amplitude, phase, and the time period at
which it repeats. Once you know these you can define the signal for all time in
the future or in the past and no information apart from this can be carried. So
all signals that carry *any* information are aperiodic. So the only sinusoids
that are of any interest are the frequency components that go to make up the
signals and also the sinewave that carries the information, which is called the
carrier. The carrier is important because it defines where in the spectrum the
signal will be transmitted over the air waves. More of that later and back to
bandwidth.
So you can analyze a signal as a bunch of sinewaves with
different frequencies and amplitudes that when added together would reconstruct
the original signal. The analysis of a signal in terms of its frequency
components is analyzing in the frequency domain and you a suitable display would
be of a graph with frequency on the horizontal axis and amplitude on the
vertical axis and there would be a graph which showed where the signal contains
frequencies and what their amplitude is.
So, finally, the bandwidth of an analogue signal is the
difference in frequency between the highest and lowest frequencies contained in
the signal. A signal might contain frequencies outside of a band that it is
supposed to use, so the signal is passed through a filter which removes the
frequency components outside of what is called the filter’s passband. For
example, the difference between the highest and lowest frequencies of the
passband will be the bandwidth of the filter. Usually, the bandwidth of a filter
will be defined as the difference between the higher and lower frequencies at
which the power is half that in its passband. A signal on the other hand might
be defined by its bandwidth between the frequencies at which its power is far
lower than half that of its passband. This is because the frequency components
at the edge of a band have to be very small (attenuated) so that they don’t
interfere with the frequency components of a signal that is transmitted in an
adjacent band.
An example of analogue bandwidth of a signal would be
the range of frequencies that contain 95% of all the power in the signal or
possibly 99% of the power of the signal.