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telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
, equalization is the reversal of distortion incurred by a signal transmitted through a channel. Equalizers are used to render the frequency response—for instance of a telephone line—''flat'' from end-to-end. When a channel has been equalized the frequency domain attributes of the signal at the input are faithfully reproduced at the output. Telephones, DSL lines and television cables use equalizers to prepare data signals for transmission. Equalizers are critical to the successful operation of electronic systems such as analog broadcast television. In this application the actual
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
of the transmitted signal must be preserved, not just its frequency content. Equalizing filters must cancel out any
group delay and phase delay In signal processing, group delay and phase delay are delay times experienced by a signal's various frequency components when the signal passes through a system that is linear time-invariant (LTI), such as a microphone, coaxial cable, amplifier, ...
between different frequency components.


Analog telecommunications


Audio lines

Early telephone systems used equalization to correct for the reduced level of high frequencies in long cables, typically using
Zobel network : ''For the wave filter invented by Zobel and sometimes named after him see m-derived filters.'' 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 publis ...
s. These kinds of equalizers can also be used to produce a circuit with a wider bandwidth than the standard telephone band of 300 Hz to 3.4 kHz. This was particularly useful for broadcasters who needed "music" quality, not "telephone" quality on landlines carrying program material. It is necessary to remove or cancel any
loading coil A loading coil or load coil is an inductor that is inserted into an electronic circuit to increase its inductance. The term originated in the 19th century for inductors used to prevent signal distortion in long-distance telegraph transmission c ...
s in the line before equalization can be successful. Equalization was also applied to correct the response of the transducers, for example, a particular
microphone A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and publ ...
might be more sensitive to low
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
sounds than to high frequency sounds, so an equalizer would be used to increase the volume of the higher frequencies (''boost''), and reduce the volume of the low frequency sounds (''cut'').


Television lines

A similar approach to audio was taken with television landlines with two important additional complications. The first of these is that the television signal is a wide bandwidth covering many more octaves than an audio signal. A television equalizer consequently typically requires more filter sections than an audio equalizer. To keep this manageable, television equalizer sections were often combined into a single network using ladder topology to form a Cauer equalizer. The second issue is that phase equalization is essential for an analog television signal. Without it
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
causes the loss of integrity of the original wave-shape and is seen as smearing of what were originally sharp edges in the picture.


Analog equalizer types

*
Zobel network : ''For the wave filter invented by Zobel and sometimes named after him see m-derived filters.'' 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 publis ...
*
Lattice phase equalizer 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 frequency, frequencies but the relative phase (waves), phase between input and output varies with frequenc ...
* Bridged T delay equalizer


Digital telecommunications

Modern digital telephone systems have less trouble in the voice frequency range as only the local line to the subscriber now remains in analog format, but DSL circuits operating in the MHz range on those same wires may suffer severe
attenuation distortion Attenuation distortion is the distortion of an analog signal that occurs during transmission when the transmission medium does not have a flat frequency response across the bandwidth of the medium or the frequency spectrum of the signal.Rowe, St ...
, which is dealt with by automatic equalization or by abandoning the worst frequencies. Picturephone circuits also had equalizers. In
digital communications Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point or ...
, the equalizer's purpose is to reduce
intersymbol interference In telecommunication, intersymbol interference (ISI) 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 a similar effect as noise, thus making ...
to allow recovery of the transmit symbols. It may be a simple
linear filter Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using ...
or a complex algorithm.


Digital equalizer types

*Linear equalizer: processes the incoming signal with a linear filter ** MMSE equalizer: designs the filter to minimize E Zero-forcing_equalizer The zero-forcing equalizer is a form of linear equalization algorithm used in communication systems which applies the inverse of the frequency response of the channel. This form of equalizer was first proposed by Robert Lucky. The zero-forcing e ...
:_approximates_the_inverse_of_the_channel_with_a_linear_filter. *
Decision_feedback_equalizer Decision may refer to: Law and politics *Judgment (law), as the outcome of a legal case *Landmark decision, the outcome of a case that sets a legal precedent * ''Per curiam'' decision, by a court with multiple judges Books * ''Decision'' (novel ...
:_augments_a_linear_equalizer_by_adding_a_filtered_version_of_previous_symbol_estimates_to_the_original_filter_output.A_tutorial_on_DFEs
_cnx.org_ * Blind_equalizer:_estimates_the_transmitted_signal_without_knowledge_of_the_channel_statistics,_using_only_knowledge_of_the_transmitted_signal's_statistics. *
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 ...
:_is_typically_a_linear_equalizer_or_a_DFE._It_updates_the_equalizer_parameters_(such_as_the_filter_coefficients)_as_it_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:_Finds_the_
maximum_likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stat ...
_(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''_(MAP)_solution._Its_goal_is_to_minimize_the_probability_that_a_given_bit_was_incorrectly_estimated. *
Turbo_equalizer In digital communications, a turbo equalizer is a type of receiver used to receive a message corrupted by a communication channel with intersymbol interference (ISI). It approaches the performance of a maximum a posteriori (MAP) receiver via iterat ...
:_applies_turbo_decoding_while_treating_the_channel_as_a_convolutional_code.


__See_also_

*
Electronic_filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
*
Weighting_filter A weighting filter is used to emphasize or suppress some aspects of a phenomenon compared to others, for measurement or other purposes. Audio applications In each field of audio measurement, special units are used to indicate a weighted measure ...
* RIAA_equalization


__References_

{{Reflist


_External_links


Interactive_demonstration_of_various_linear_and_non-linear_equalizersInteractive_demonstration_of_a_Viterbi_equalizer
Signal_processinghtml" ;"title="e, 2], where e is the error signal, which is the filter output minus the transmitted signal. **
Zero-forcing equalizer The zero-forcing equalizer is a form of linear equalization algorithm used in communication systems which applies the inverse of the frequency response of the channel. This form of equalizer was first proposed by Robert Lucky. The zero-forcing e ...
: approximates the inverse of the channel with a linear filter. *
Decision feedback equalizer Decision may refer to: Law and politics *Judgment (law), as the outcome of a legal case *Landmark decision, the outcome of a case that sets a legal precedent * ''Per curiam'' decision, by a court with multiple judges Books * ''Decision'' (novel ...
: augments a linear equalizer by adding a filtered version of previous symbol estimates to the original filter output.A tutorial on DFEs
cnx.org * Blind equalizer: estimates the transmitted signal without knowledge of the channel statistics, using only knowledge of the transmitted signal's statistics. *
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 ...
: is typically a linear equalizer or a DFE. It updates the equalizer parameters (such as the filter coefficients) as it 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: Finds the
maximum likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stat ...
(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'' (MAP) solution. Its goal is to minimize the probability that a given bit was incorrectly estimated. *
Turbo equalizer In digital communications, a turbo equalizer is a type of receiver used to receive a message corrupted by a communication channel with intersymbol interference (ISI). It approaches the performance of a maximum a posteriori (MAP) receiver via iterat ...
: applies turbo decoding while treating the channel as a convolutional code.


See also

*
Electronic filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
*
Weighting filter A weighting filter is used to emphasize or suppress some aspects of a phenomenon compared to others, for measurement or other purposes. Audio applications In each field of audio measurement, special units are used to indicate a weighted measure ...
* RIAA equalization


References

{{Reflist


External links


Interactive demonstration of various linear and non-linear equalizersInteractive demonstration of a Viterbi equalizer
Signal processing>e, 2 where e is the error signal, which is the filter output minus the transmitted signal. **
Zero-forcing equalizer The zero-forcing equalizer is a form of linear equalization algorithm used in communication systems which applies the inverse of the frequency response of the channel. This form of equalizer was first proposed by Robert Lucky. The zero-forcing e ...
: approximates the inverse of the channel with a linear filter. *
Decision feedback equalizer Decision may refer to: Law and politics *Judgment (law), as the outcome of a legal case *Landmark decision, the outcome of a case that sets a legal precedent * ''Per curiam'' decision, by a court with multiple judges Books * ''Decision'' (novel ...
: augments a linear equalizer by adding a filtered version of previous symbol estimates to the original filter output.A tutorial on DFEs
cnx.org * Blind equalizer: estimates the transmitted signal without knowledge of the channel statistics, using only knowledge of the transmitted signal's statistics. *
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 ...
: is typically a linear equalizer or a DFE. It updates the equalizer parameters (such as the filter coefficients) as it 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: Finds the
maximum likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stat ...
(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'' (MAP) solution. Its goal is to minimize the probability that a given bit was incorrectly estimated. *
Turbo equalizer In digital communications, a turbo equalizer is a type of receiver used to receive a message corrupted by a communication channel with intersymbol interference (ISI). It approaches the performance of a maximum a posteriori (MAP) receiver via iterat ...
: applies turbo decoding while treating the channel as a convolutional code.


See also

*
Electronic filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
*
Weighting filter A weighting filter is used to emphasize or suppress some aspects of a phenomenon compared to others, for measurement or other purposes. Audio applications In each field of audio measurement, special units are used to indicate a weighted measure ...
* RIAA equalization


References

{{Reflist


External links


Interactive demonstration of various linear and non-linear equalizersInteractive demonstration of a Viterbi equalizer
Signal processing