About Adaptive Equalizers

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Hi Hunter,
Sorry because I din't answer to your question about post #2.
You are right. The response has a main lobe preceded by precursors and followed by a "tail".

Z
 


In the expression \[z=e^{jw}\], \[w\] is the normalized angular frequency, measured in radians/sample.
In \[z=e^{jwT}\] it is the angular frequency, measured in radians/seconds.
Regards

Z
 

After a second thought: why the receiver waits \[N_1\] samples in the first place? Can we say that the reason for delaying is to get a factorized transfer function to realize the noise whitening filter, for example??

---------- Post added at 04:13 ---------- Previous post was at 04:09 ----------
zorro said:
In the expression \[z=e^{jw}\], \[w\] is the normalized angular frequency, measured in radians/sample.
In \[z=e^{jwT}\] it is the angular frequency, measured in radians/seconds.
Regards

Z
Click to expand...

Thanks. About the noise whitening filter transfer function, can we say that we choose \[1/G^*(1/z^*)\] as the transfer function of the noise whitening filter because it will be causal, since \[G^*(1/z^*)\] is anti causal? prof. Proakis says that this filter is causal and stable. Why stable?
 

hunter555persia said:
Because after waiting for N1 samples those future samples needed for equalization will be received and stored.
Click to expand...

But again, if we did not wait \[N_1\] samples, there will be no interference with them, physically speaking. Right?
 

Yeah I don't understand this. ISI can't come from future samples physically, but in the formulation of text book there are future samples as well.
?????????????????????!!!!!!!!!!!!!!!!!!!
 

I think it has to do with the whitening filter, because if we do not have future samples, then we can not factorize the effective channel. It is still confusing!!
 

Hi guys,

About "future samples": as I said before, the pulse has precursors and tail (postcursors). The precursors are the samples of the response before the peak, and they can span over several symbols.
When you are detecting a current symbol, the ISI is composed by the postcursors of the past simbols as well as the precursors of the future ones.
Regards

Z
 


When transmitting this future symbols, how they interfere with current symbol? I mean, can the next symbols (or part of them) arrive with the current symbol because the channel is dispersive?
 

David83 said:
... can the next symbols (or part of them) arrive with the current symbol because the channel is dispersive?
Click to expand...
Yes. The channel is causal but there is a delay to the peak of the response. Think for example in a relatively slow response (long rise time).
Z
 

zorro is right. Channel causes different signal components to have different delays. So the short delay components of the current symbol are influenced by the long delay components of the next symbol.
 

EDIT for post #31: Channel causes different signal components to have different delays. So the LONG delay components of the current symbol are influenced by the SHORT delay components of the next symbol.
 

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