Bandwidth of a Signal – Bandwidth of a Channel

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BANDWIDTH OF A SIGNAL

  • Bandwidth can be defined as the portion of the electromagnetic spectrum occupied by the signal
    It may also be defined as the frequency range over which a signal is transmitted.
  • Different types of signals have different bandwidth. Ex. Voice
    signal, music signal, etc Bandwidth of analog and digital signals are calculated in separate ways; analog signal bandwidth is measured in terms of its frequency (hz) but digital signal bandwidth is measured in terms of bit rate (bits per second, bps) Bandwidth of signal is different from bandwidth of the medium/channel

Bandwidth of an analog signal

  • Bandwidth of an analog signal is expressed in terms of its
    frequencies.
  • It is defined as the range of frequencies that the composite
    analog signal carries.
  • It is calculated by the difference between the maximum
    frequency and the minimum frequency

Bandwidth of a digital signal

  • It is defined as the maximum bit rate of the signal to be
    transmitted.
  • It is measured in bits per second.

BANDWIDTH OF A CHANNEL

  • A channel is the medium through which the signal carrying information will be passed.
  • In terms of analog signal, bandwidth of the channel is the range of frequencies that the channel can carry.
    In terms of digital signal, bandwidth of the channel is the maximum bit rate supported by the channel. i.e. the
    maximum amount of data that the channel can carry per  second.
  • The bandwidth of the medium should always be greater than the bandwidth of the signal to be transmitted else the transmitted signal will be either attenuated or distorted or both leading in loss of information.
  • The channel bandwidth determines the type of signal to be transmitted i.e. analog or digital.

THE MAXIMUM DATA RATE OF A CHANNEL

Data rate depends on three factors:

1. The bandwidth available
2. The level of the signals we use
3. The quality of the channel (the level of noise)

The quality of the channel indicates two types:

a) A Noiseless or Perfect Channel
An ideal channel with no noise.
The Nyquist Bit rate derived by Henry Nyquist
gives the bit rate for a Noiseless Channel.
b) A Noisy Channel
A realistic channel that has some noise.
The Shannon Capacity formulated by Claude
Shannon gives the bit rate for a Noisy Channel

Nyquist Bit Rate
The Nyquist bit rate formula defines the theoretical maximum bit rate for a noiseless channel

nyquist-bit-rate
Where,

  • Bitrate is the bitrate of the channel in bits per second
  • Bandwidth is the bandwidth of the channel
  • L is the number of signal levels.

Example:
What is the maximum bit rate of a noiseless channel with a bandwidth of 5000 Hz transmitting a signal with two signal
levels.

Solution:
The bit rate for a noiseless channel according to Nyquist Bit rate can be calculated as follows:
  BitRate = 2 x Bandwidth x Log2 L
                  = 2 x 5000 x log2 2 =10000 bps

 

Shannon Capacity
The Shannon Capacity defines the theoretical maximum bit rate for a noisy channel

shannon-capacity
Where,

  • Capacity is the capacity of the channel in bits per second
  • Bandwidth is the bandwidth of the channel
  • SNR is the Signal to Noise Ratio

Shannon Capacity for calculating the maximum bit rate for a noisy channel does not consider the number of levels of the signals being transmitted as done in the Nyquist bit rate.

Example: Calculate the bit rate for a noisy channel with SNR 300 and bandwidth of 3000Hz

Solution:
The bit rate for a noisy channel according to Shannon
Capacity can be calculated as follows:
Capacity=bandwidth X log2 (1 +SNR)
= 3000 x log2 (1 + 300)
= 3000 x log2 ( 301)
= 3000 x 8.23
= 24,690bps

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