In telecommunication

Telecommunication

Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...

, the equalizer is a device that attempts to reverse the distortion incurred by a signal transmitted through a channel

Channel (communications)

In telecommunications and computer networking, a communication channel, or channel, refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel...

.

Digital communications

In digital communications, its purpose is to reduce intersymbol interference

Intersymbol interference

In telecommunication, intersymbol interference is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable...

 to allow recovery of the transmit symbols. It may be a simple linear filter

Linear filter

Linear filters in the time domain process time-varying input signals to produce output signals, subject to the constraint of linearity.This results from systems composed solely of components classified as having a linear response....

 or a complex algorithm. The following equalizer types are commonly used in digital communications:

• Linear Equalizer: processes the incoming signal with a linear filter
  • MMSE equalizer
    Wiener deconvolution
    In mathematics, Wiener deconvolution is an application of the Wiener filter to the noise problems inherent in deconvolution. It works in the frequency domain, attempting to minimize the impact of deconvoluted noise at frequencies which have a poor signal-to-noise ratio.The Wiener deconvolution...
    
    : designs the filter to minimize E[|e|²], where e is the error signal, which is the filter output minus the transmitted signal.
  • Zero Forcing Equalizer
    Zero Forcing Equalizer
    Zero Forcing Equalizer refers to a form of linear equalization algorithm used in communication systems which inverts the frequency response of the channel. This form of equalizer was first proposed by Robert Lucky....
    
    : approximates the inverse of the channel with a linear filter.
• Decision Feedback Equalizer: augments a linear equalizer by adding a filtered version of previous symbol estimates to the original filter output.
• Blind Equalizer
  Blind equalization
  Blind equalization is a digital signal processing technique in which the transmitted signal is inferred from the received signal, while making use only of the transmitted signal statistics. Hence, the use of the word blind in the name....
  
  : estimates the transmitted signal without knowledge of the channel statistics, using only knowledge of the transmitted signal's statistics.
• Adaptive Equalizer
  Adaptive equalizer
  An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. It is frequently used with coherent modulations such as phase shift keying, mitigating the effects of multipath propagation and Doppler spreading.Many adaptation strategies exist...
  
  : is typically a linear equalizer or a DFE. It updates the equalizer parameters (such as the filter coefficients) as it is processes the data. Typically, it uses the MSE cost function; it assumes that it makes the correct symbol decisions, and uses its estimate of the symbols to compute e, which is defined above.
• Viterbi Equalizer
  Viterbi algorithm
  The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states – called the Viterbi path – that results in a sequence of observed events, especially in the context of Markov information sources, and more generally, hidden Markov models...
  
  : Finds the maximum likelihood
  Maximum likelihood
  In statistics, maximum-likelihood estimation is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters....
  
   (ML) optimal solution to the equalization problem. Its goal is to minimize the probability of making an error over the entire sequence.
• BCJR Equalizer: uses the BCJR algorithm (also called the Forward-backward algorithm) to find the maximum a posteriori
  Maximum a posteriori
  In Bayesian statistics, a maximum a posteriori probability estimate is a mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data...
  
   (MAP) solution. Its goal is to minimize the probability that a given bit was incorrectly estimated.
• Turbo equalizer
  Turbo equalizer
  -History:- Standard Communication System Overview :-Turbo Equalizer Overview:- External links :* includes an annotated bibliography, interactive block diagram, and turbo equalization simulation code.* a Signal Processing Magazine primer on turbo equalization...
  
  : applies turbo decoding while treating the channel as a convolutional code.

Analogue communications

Below is a list of equalizers with applications in analogue communications:

• Zobel network
  Zobel network
  Zobel networks are a type of filter section based on the image impedance design principle. They are named after Otto Zobel of Bell Labs who published a much referenced paper on image filters in 1923. The distinguishing feature of Zobel networks is that the input impedance is fixed in the design...
  
  
• Lattice phase equaliser
  Lattice phase equaliser
  A lattice phase equaliser or lattice filter is an example of an all-pass filter. That is, the attenuation of the filter is constant at all frequencies but the relative phase between input and output varies with frequency...
  
  
• Bridged T delay equaliser
  Bridged T delay equaliser
  thumbThe bridged-T delay equaliser is an electrical all-pass filter circuit utilising bridged-T topology whose purpose is to insert an, ideally, constant delay at all frequencies in the signal path. It is a class of image filter.-Applications:...