- Adaptive equalizer
An adaptive equalizer is a filter that adaptively updates its coefficients in order to track a time-varying communication channel. It is frequently used with coherent modulations such as

phase shift keying in wireless communications, mitigating the effects of multipath propagation and Doppler spreading. Many varieties exist. A well-known example is the decision feedback equalizer, a filter that uses feedback of detected symbols in addition to conventional equalization of future symbols.An adaptive equalizer is an example of a time variant system.

**What is a Time Variant system ?**It's a system whose characteristics change with time.If we assume that the input of a certain system is x(t) and the output is y(t),and if we assume that the relation between both is y(t)=ʎ(t)*x(t)

Given that ʎ is a function of time [ ʎ(t)] ,and since the value of ʎ changes..then the gain of the above relation changes with time.

**Example**Assume that at time ( t=0 ) ,ʎ(0)=10 ,x(t)=50 accordingly y(t)=50*10=500 at time (t=10s) ,ʎ(10)=30 ,x(t)=50 accordingly y(t)=50*30=1500

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"What do we notice from this example ?"

For the same input [x(t)=50] ;the output [y(t)] changed.

a system of this nature is called

**Time Variant**. So in case of**Adaptive Equalizer**the gain of the circuit changes with time so as to adjust the value of the output to a certain level.To make this clearer..the gain [ʎ(t)] changes to adjust the output [y(t)] to a preset level,so any change in the input [x(t)] has no effect on the output.

**Example**The output [y(t)] of an adaptive equalizer must be set to 100. 1. x(10s)=10 then ʎ(t)=100/10 = 10 2. x(50s)=25 then ʎ(t)=100/25 = 4 and so on So that it's clear now that the value of ʎ changes to set the value of the output to its preset value.

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