Transcript Bandwidth - Studyeland

Bandwidth
• Signal bandwidth:
– We can divide signals into two categories: The pure
tone signal (the sinusoidal wave, consisting of one
frequency component), and complex signals that
are composed of several components, or sinusoids
of various frequencies.
T=1x10-3 s
0
1
Pure signal
f=1/1x10-3
=1000Hz=1 kHz
t (ms)
The bandwidth of a signal composed of components
of various frequencies (complex signal) is the
difference between its highest and lowest frequency
components, and is expressed in Hertz (Hz) - the
same as frequency.
For example, a square wave may be constructed by
adding sine waves of various frequencies:
Pure tone
150 Hz sine wave
Pure tone
450 Hz sine wave
Approaching a 150 Hz
square wave
(ms)
The resulting wave resembles a square wave. If more
sine waves of other frequencies were added, the
resulting waveform would more closely resemble a
square wave
Since the resulting wave contains 2 frequency
components, its bandwidth is around 450-150=300
Hz.
Channel bandwidth:
– The bandwidth of a channel (medium) is defined to be the
range of frequencies that the medium can support. Bandwidth
is measured in Hz
– With each transmission medium, there is a frequency range of
electromagnetic waves that can be transmitted:
Increasing
bandwidth
» Twisted pair cable: 0 to 109 Hz (Bandwidth : 109 Hz)
» Coax cable: 0 to 1010 Hz (Bandwidth : 1010 Hz)
» Optical fiber: 1014 to 1016 Hz (Bandwidth : 1016 -1014 =
9.9x1015 Hz)
– Optical fibers have the highest bandwidth (they can support
electromagnetic waves with very high frequencies, such as
light waves)
– The bandwidth of the channel dictates the information
carrying capacity of the channel
– This is calculated using Shannon’s channel capacity formula
The bandwidth of a composite signal is the difference
between the highest and the lowest frequencies
contained in that signal.
•Spectrum
(range of frequencies)
•Absolute bandwidth: width of spectrum
•Bandwidth
(width of the spectrum)
•Two composite signals with different spectrums might
have the same bandwidth.
Signal A [10,20] vs. Signal B [90,100]
The bandwidth of periodic and nonperiodic composite signals
Example
If a periodic signal is decomposed into five sine waves
with frequencies of 100, 300, 500, 700, and 900 Hz, what
is its bandwidth? Draw the spectrum, assuming all
components have a maximum amplitude of 10 V.
Solution
Let fh be the highest frequency, fl the lowest frequency,
and B the bandwidth. Then
The spectrum has only five spikes, at 100, 300, 500, 700,
and 900 Hz
Bandwidth for above example
Example
A non periodic composite signal has a bandwidth of
200 kHz, with a middle frequency of 140 kHz and
peak amplitude of 20 V. The two extreme
frequencies have an amplitude of 0. Draw the
frequency domain of the signal.
Solution
Let fh be the highest frequency, and fl the lowest
frequency. Then
fh – fl = 200
(fh+fl)/2 = 140
The lowest frequency must be at 40 kHz and the
highest at 240 kHz.
Bandwidth for above example
In networking, we use the term
bandwidth in two contexts
• The first, bandwidth in Hertz, refers to the
range of frequencies in a composite signal or the
range of frequencies that a channel can pass.
•The second, bandwidth in bits per second,
refers to the speed of bit transmission in a
channel or link.
Signal-to-Noise Ratio
• S/N is normally measured in dB (decibel). It is a
relationship between the signal we want versus the
noise that we do not want, which is in the medium.
• It can be thought of as a fractional relationship (that
is, before we take the logarithm):
Decibel: measures the relative strengths of two
signals or one signal at two different points.
dB  10log10
P2
P1
It is negative if a signal is attenuated and positive if a
signal is amplified
SNR = Average signal power/Average noise power
SNRdB  10log10 SNR
Example
Consider an extremely noisy channel in which the value
of the signal-to-noise ratio is almost zero. In other
words, the noise is so strong that the signal is faint. For
this channel the capacity C is calculated as
This means that the capacity of this channel is zero
regardless of the bandwidth. In other words, we cannot
receive any data through this channel.
Example
We can calculate the theoretical highest bit rate of a
regular telephone line. A telephone line normally has a
bandwidth of 3000. The signal-to-noise ratio is usually
3162. For this channel the capacity is calculated as
This means that the highest bit rate for a telephone line is
34.860 kbps. If we want to send data faster than this, we
can either increase the bandwidth of the line or improve
the signal-to-noise ratio.
For practical purposes, when the SNR is very high, we can
assume that SNR + 1 is almost the same as SNR. In these
cases, the theoretical channel capacity can be simplified to
For example, The signal-to-noise ratio is often given in
decibels. Assume that SNRdB = 36 and the channel
bandwidth is 2 MHz. Calculate theoretical channel
capacity
Digital Signals
In addition to being represented by an analog
signal, information can also be represented by a
digital signal. For example, a 1 can be encoded as
a positive voltage and a 0 as zero voltage. A digital
signal can have more than two levels. In this case,
we can send more than 1 bit for each level.
Frequency Vs Bit Rate
Frequency: The number of periods in 1 sec.
Bit rate: The number of bits sent in 1sec, expressed in
bits per second (bps).
Bits per second (bps): The number of bits transmitted
across a medium in a given second.
Baud rate: The number of times a signal changes value
per second.
bps and baud rate are not always the same.
Two digital signals: one with two levels and the other
with four signal levels
Example
A digital signal has eight levels. How many bits are
needed per level?
We calculate the number of bits from the formula
Each signal level is represented by 3 bits.
Example
What is the bit rate for high-definition TV (HDTV)?
Solution
HDTV uses digital signals to broadcast high quality video
signals. The HDTV screen is normally a ratio of 16 : 9.
There are 1920 by 1080 pixels per screen, and the screen
is renewed 30 times per second. Twenty-four bits
represents one color pixel.
The TV stations reduce this rate to 20 to 40 Mbps through
compression.
Baseband
A baseband is an adjective that describes signals and
systems whose range of frequencies is measured from
zero to a maximum bandwidth or highest signal
frequency; it is sometimes used as a noun for a band of
frequencies starting at zero. It can often be considered
as synonym to low pass, and antonym to passband.
Baseband transmission: sending a digital signal
over a channel without changing the digital signal
to an analog signal.
•If we need to send bits faster, we need more bandwidth.