# Equalizer

Started by June 11, 2007
```I have two complex signals (Input and output) of a channel I need to
equalize. I can have 2 linear equalizers one for the real part and one for
the imaginary and train them independently or I can use one complex
equalizer and train it using the complex signal. My questions are which one
is better? Is there any advantage of one on the other or they are equivalent
?

Regards

Tom

```
```
Tom wrote:

> I have two complex signals (Input and output) of a channel I need to
> equalize. I can have 2 linear equalizers one for the real part and one for
> the imaginary and train them independently

^^^^^^^^^^^^^^^^^^^^^^

This is completely wrong.

> or I can use one complex
> equalizer and train it using the complex signal.  My questions are which one
> is better? Is there any advantage of one on the other or they are equivalent

If you are working with the real signal, you should use the real
equalizer. If you are working with the complex signal, you use the
complex equalizer. Which way is preferred depends on the application.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```Why the first option can not work ?

"Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
news:8Aebi.25140\$YL5.22280@newssvr29.news.prodigy.net...
>
>
> Tom wrote:
>
>> I have two complex signals (Input and output) of a channel I need to
>> equalize. I can have 2 linear equalizers one for the real part and one
>> for the imaginary and train them independently
>
> ^^^^^^^^^^^^^^^^^^^^^^
>
> This is completely wrong.
>
>
>> or I can use one complex equalizer and train it using the complex signal.
>> My questions are which one
>> is better? Is there any advantage of one on the other or they are
>> equivalent
>
> If you are working with the real signal, you should use the real
> equalizer. If you are working with the complex signal, you use the complex
> equalizer. Which way is preferred depends on the application.
>
>
>
> DSP and Mixed Signal Design Consultant
>
> http://www.abvolt.com

```
```Becase the phase shift is different at the different frequencies.

VLV

Tom wrote:
> Why the first option can not work ?
>
> "Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
> news:8Aebi.25140\$YL5.22280@newssvr29.news.prodigy.net...
>
>>
>>Tom wrote:
>>
>>
>>>I have two complex signals (Input and output) of a channel I need to
>>>equalize. I can have 2 linear equalizers one for the real part and one
>>>for the imaginary and train them independently
>>
>>^^^^^^^^^^^^^^^^^^^^^^
>>
>>This is completely wrong.
>>
>>
>>
>>>or I can use one complex equalizer and train it using the complex signal.
>>>My questions are which one
>>>is better? Is there any advantage of one on the other or they are
>>>equivalent
>>
>>If you are working with the real signal, you should use the real
>>equalizer. If you are working with the complex signal, you use the complex
>>equalizer. Which way is preferred depends on the application.
>>
>>
>>
>>DSP and Mixed Signal Design Consultant
>>
>>http://www.abvolt.com
>
>
>
```
```What if I transform the real and imaginary to Amplitude and phase signals
and use them to train 2 equalizers separately and then transform back the
output of the equalizers to real and Imaginary signals. Will this work in
theory ?

regards

Tom
"Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
news:mggbi.13524\$2v1.1260@newssvr14.news.prodigy.net...
> Becase the phase shift is different at the different frequencies.
>
> VLV
>
>
> Tom wrote:
>> Why the first option can not work ?
>>
>> "Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
>> news:8Aebi.25140\$YL5.22280@newssvr29.news.prodigy.net...
>>
>>>
>>>Tom wrote:
>>>
>>>
>>>>I have two complex signals (Input and output) of a channel I need to
>>>>equalize. I can have 2 linear equalizers one for the real part and one
>>>>for the imaginary and train them independently
>>>
>>>^^^^^^^^^^^^^^^^^^^^^^
>>>
>>>This is completely wrong.
>>>
>>>
>>>
>>>>or I can use one complex equalizer and train it using the complex
>>>>signal. My questions are which one
>>>>is better? Is there any advantage of one on the other or they are
>>>>equivalent
>>>
>>>If you are working with the real signal, you should use the real
>>>equalizer. If you are working with the complex signal, you use the
>>>complex equalizer. Which way is preferred depends on the application.
>>>
>>>
>>>
>>>DSP and Mixed Signal Design Consultant
>>>
>>>http://www.abvolt.com
>>
>>

```
```"Tom" <tomdarel@yahoo.com> wrote in message
news:466d725c\$0\$12085\$c3e8da3@news.astraweb.com...
> I have two complex signals (Input and output) of a channel I need to
> equalize. I can have 2 linear equalizers one for the real part and one for
> the imaginary and train them independently or I can use one complex
> equalizer and train it using the complex signal. My questions are which
one
> is better? Is there any advantage of one on the other or they are
equivalent
> ?
>
> Regards
>
> Tom
>
>

Unless you have absolutlely zero carrier offset (which is impossible if
either receiver or transmitter is moving) you can not adapt real and
imaginary independently. I think you have to use a complexe equalizer. That
said, there are ways to implement the complex multiply with only three real
multiplies, but I don't think that is where you were heading.

-Clark

```
```Once you convert to magnitude and phase the operations are no longer linear,
right? The phase at least is modulo 2 pi.

The equalizer is just a filter. The filter can be applied in time or
frequency domain. In the frequency domain an FFT would need to convert the
time waveform to frequency domain, then multiply by the FFT of the equalizer
filter, and do an inverse FFT to get back to time.

But I don't see any way to convolve the data and the filter in
magnitude/phase terms?

-Clark

"Tom" <tomdarel@yahoo.com> wrote in message
news:466db4d4\$0\$10511\$c3e8da3@news.astraweb.com...
> What if I transform the real and imaginary to Amplitude and phase signals
> and use them to train 2 equalizers separately and then transform back the
> output of the equalizers to real and Imaginary signals. Will this work in
> theory ?
>
> regards
>
> Tom
> "Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
> news:mggbi.13524\$2v1.1260@newssvr14.news.prodigy.net...
> > Becase the phase shift is different at the different frequencies.
> >
> > VLV
> >
> >
> > Tom wrote:
> >> Why the first option can not work ?
> >>
> >> "Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
> >> news:8Aebi.25140\$YL5.22280@newssvr29.news.prodigy.net...
> >>
> >>>
> >>>Tom wrote:
> >>>
> >>>
> >>>>I have two complex signals (Input and output) of a channel I need to
> >>>>equalize. I can have 2 linear equalizers one for the real part and one
> >>>>for the imaginary and train them independently
> >>>
> >>>^^^^^^^^^^^^^^^^^^^^^^
> >>>
> >>>This is completely wrong.
> >>>
> >>>
> >>>
> >>>>or I can use one complex equalizer and train it using the complex
> >>>>signal. My questions are which one
> >>>>is better? Is there any advantage of one on the other or they are
> >>>>equivalent
> >>>
> >>>If you are working with the real signal, you should use the real
> >>>equalizer. If you are working with the complex signal, you use the
> >>>complex equalizer. Which way is preferred depends on the application.
> >>>
> >>>
> >>>
> >>>DSP and Mixed Signal Design Consultant
> >>>
> >>>http://www.abvolt.com
> >>
> >>
>

```
```My signal does not have a carrier, it is a baseband. do I still have to use
a complex equalizer ?
"cpope" <cepope@nc.rr.com> wrote in message
>
> "Tom" <tomdarel@yahoo.com> wrote in message
> news:466d725c\$0\$12085\$c3e8da3@news.astraweb.com...
>> I have two complex signals (Input and output) of a channel I need to
>> equalize. I can have 2 linear equalizers one for the real part and one
>> for
>> the imaginary and train them independently or I can use one complex
>> equalizer and train it using the complex signal. My questions are which
> one
>> is better? Is there any advantage of one on the other or they are
> equivalent
>> ?
>>
>> Regards
>>
>> Tom
>>
>>
>
> Unless you have absolutlely zero carrier offset (which is impossible if
> either receiver or transmitter is moving) you can not adapt real and
> imaginary independently. I think you have to use a complexe equalizer.
> That
> said, there are ways to implement the complex multiply with only three
> real
> multiplies, but I don't think that is where you were heading.
>
> -Clark
>
>

```
```On Jun 11, 6:58 pm, "John" <j...@excite.com> wrote:
> My signal does not have a carrier, it is a baseband. do I still have to use
> a complex equalizer ?"cpope" <cep...@nc.rr.com> wrote in message
>

Even though it's at baseband, in any practical system, your signal is
probably going to be transmitted on a carrier at some point. Your
receiver's LO is going to have some frequency error with respect to
your transmitter's oscillator, which will cause a low-frequency
can correct this if the error is small enough, but it needs both the
real and imaginary components to do so (since the modulation caused by
the frequency error is complex).

Why are you so averse to implementing a complex equalizer anyway? The
underlying structure is the same; you just need to allow all
quantities to be complex and remember to put in complex conjugates at
the right places, depending on the equalizer's type.

Jason

```
```cincydsp@gmail.com wrote:
> On Jun 11, 6:58 pm, "John" <j...@excite.com> wrote:
>> My signal does not have a carrier, it is a baseband. do I still have to use
>> a complex equalizer ?"cpope" <cep...@nc.rr.com> wrote in message
>>
>
> Even though it's at baseband, in any practical system, your signal is
> probably going to be transmitted on a carrier at some point. Your
> receiver's LO is going to have some frequency error with respect to
> your transmitter's oscillator, which will cause a low-frequency
> can correct this if the error is small enough, but it needs both the
> real and imaginary components to do so (since the modulation caused by
> the frequency error is complex).
>
> Why are you so averse to implementing a complex equalizer anyway? The
> underlying structure is the same; you just need to allow all
> quantities to be complex and remember to put in complex conjugates at
> the right places, depending on the equalizer's type.

I think he wants to know the difference between a complex filter (that
obviously has real and imaginary parts) and two filters, one for the
real part of the signal and another for the imaginary part. Do do I.

Jerry
--
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```