Sampling Theorem and Encoding in Digital Communication | 3+ Important facts

Sampling Theorem and Encoding in Digital Communication

Topic of Discussion: Digital Communication

  • Introduction to Digital Communication
  • It’s advantages over Analog communication
  • What is Encoding
  • Types of Encoding
  • Companding in Encoding
  • Sampling Theorem

To know about encoding and other features, first, we have to recall what digital communication is and some of its advantages.

What is Digital Communication?

Definition & the advantages of Digital communication:

It is the type of communication system, in which the signals which are used to transmit data or information, should be discrete in time & amplitude. They are also called digital signals

Digital Communication system

Some of the important advantages are:

  • Digital communications provide increased immunity to noise and external interference.
  • It offers better flexibility and compatibility.
  • Digital communication gives improved reliability due to channel coding.
  • Digital Communication system is comparatively simpler and cheaper than an analog communication system.
  • Computers can be used directly for digital signal processing.
  • It makes communication more secured using data encryption.
  • Wideband channels are available for digital communications.

What is Encoding?

Encoding in digital communication

Introduction to encoding in digital communication:

Encoding is a special type of process in which various patterns or voltages or current levels are used to represent 1s and 0s of the digital signals on a particular transmission link or channel.

What are the different types of encoding?

There are four types of encoding; they are-

  • Unipolar
  • Polar
  • Bipolar
  • Manchester

What is Companding?

Why is Companding needed in encoding?

Quantization is of two types

  • Uniform Quantization,
  • Non-Uniform Quantization.

Non-Uniform quantization is achieved through companding. This is a process in which compression of the input signal is done in the transmitter, whereas the expansion of the signal is done at the receiver. The combination of compressing and expanding is companding.

The process of Companding:

In a linear or uniform quantization, the small amplitude signals would have a poor SNR than the large-amplitude signals. This is a drawback of linear quantization. To remove this problem, non-uniform quantization is utilized in which the step size differs with the amplitude of the i/p. The step size variation is achieved by distorting the input signal before the quantization process. This process of distorting the input signal before quantization is known as compression, in which the signal is amplified at low signal level and attenuated at high signal level.

After compression, uniform quantization is applied. Here the signal is companding, which is to make the overall transmission distortion less.

Input Output characteristics of a Compander:

What is Aliasing?

Define the Aliasing Effect:

  • Aliasing is an important term in encoding & digital communication itself.
  • If signal is sampled at a rate lesser than the Nyquist Rate, the side band overlap, producing an interference-effect. This is called the Aliasing Effect.
  • If aliasing takes place, it is not possible to recover the original analog signal.
Aliasing Effect

Anti-Aliasing Filter:

To remove the problem of the aliasing from the signals, a special type of filter is used, which is known as the Anti- Aliasing Filter.

An anti-aliasing filter is usually at the input of a PAM generator to avoid the effect of aliasing. PAM signal is generated by sampling the input analog signal in a sampler circuit.

The sampling is thru in accord with the Sampling Theorem , i.e., the sampling frequency fs is kept equal to or higher than twice the maximum frequency W present in the input analog signal. If, however, fs<2W, then aliasing occurs, and recovery of the original analog signal will not be possible. Since fs is usually kept unchanged, the input analog signal is passed through a low pass filter before sampling to band limit the analog signal in conformity with the sampling theorem.

What is Sampling?

State Sampling Theorem:

The mathematical basis of the sampling process has been laid by the Nyquist sampling theorem. It also gives an idea about the recovery of the original signal completely from its samples. The statement of the sampling theorem is thus given in two parts below’;

  • A band-limiting signal of finite energy that has no freq. rage of W Hz is usualy designated by agreeing the value of the signals at that time parted by ½ W sec.
  • A band-limit signal of finite energy that has no freq. components outside the W Hz might be totally reformed from the information of its sample data rated @2W sample/sec.

The sampling rate 2W/sec is entitled as the “Nyquist Rate.” in the Sampling Theorem explanation.

The reciprocal 1/2W is entitled “Nyquist Interval.”

Nyquist Shannon sampling theorem
Nyquist–Shannon sampling theorem, Image Credit – anonymous, AliasedSpectrum, marked as public domain, more details on Wikimedia Commons

How does sampling theorem work in encoding?

In sampling theorem, the received message (baseband) signals are sampled with a typical combination of rectangular-shaped or square-shaped pulses. For the accurate reconstruction of the message signal in the receiving end, the sampling rate has to be more than double of maximum freq. component specified by ‘W’. In a practical case, an anti-aliasing filter (lpf) is utilized at the sampler device to discard the frequencies band those are greater than the W. Hence, the various utilization of sampling allows the minimization of the incessantly changeable message signal (of some determinate period) to some degree of discrete quantity per sec.

Explain the Encoding Process:

In merging the sampling theorem and quantization procedures, the order of a continuous message (baseband) signal converts limited to discrete values but not in the procedure appropriate for the transmission over a long-distanced radio telecommunication channel. To utilize the benefits of sampling and quantization to create the communicated signal stronger to noise, interference, and other channel dreadful conditions. The main requirement is an encoding process to interpret the discrete set of sample values to a proper form of signal. This distinct procedure in a code is called a code element or symbol. Specific prearrangement of symbols employed in coding to signify a single value of the distinctive set is entitled as ‘codeword’ or ‘character’.

In binary encryption, the symbol is in two distinctive values, such as a -ve pulse or a +ve pulse. The binary codes are, as a matter of course, signified as 0 and 1 combination only.

Actually, a binary code is favored over other codes such as ternary cod for the following grounds.

  • The more significant advantages over the effects of noise in a transmission channel could be obtained using a binary code because of its sustainability with higher noises.
  • Another reason is the binary code is comparatively simplified to produce and to regenerate again.

What is A-law and μ-law in companding?

There are two types of compression laws in use. These are, namely, 𝞵 law & A-law companding.

𝞵 law companding is used in various country A-law companding recommended by CCITT is used in asian and European countries.

𝞵 law is defined by the expression-

The A-law compression characteristic is finished up of a linear segment for low-level input and a log-segment for higher level input. The special case A=1 corresponds to uniform quantization. A applied value for A is 87.561.

A-law companding is inferior to 𝞵 law in terms of small-signal quality, i.e., ideal channel noise.

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