# Hilbert transform vs quadrature processing

Started by September 17, 2009
```Hi, all

I want to demodulate an IF real signal and it seems that there are some
different methods on it. I can employ hilbert transform to construct the
analytic signal and downconvert it to baseband. Otherwise, I can get the
signal multiplied by a sine and a cosine which oscillate at IF carrier
frequency and then lowpass-filter unwanted parts. These two methods now
also deal with complex numbers.

What is the difference between these two methods? I can't tell which is
superior.

```
```
alomar wrote:
> Hi, all
>
> I want to demodulate an IF real signal and it seems that there are some
> different methods on it. I can employ hilbert transform to construct the
> analytic signal and downconvert it to baseband. Otherwise, I can get the
> signal multiplied by a sine and a cosine which oscillate at IF carrier
> frequency and then lowpass-filter unwanted parts. These two methods now
> also deal with complex numbers.
>
> What is the difference between these two methods?

As long as you can separate the mirror images, both methods are equvalent.

> I can't tell which is superior.

You have to use Hilbert transform if the image spectrum overlaps with
the downconverted spectrum.

DSP and Mixed Signal Design Consultant
http://www.abvolt.com
```
```
alomar wrote:

> Hi, all
>
> I want to demodulate an IF real signal and it seems that there are some
> different methods on it. I can employ hilbert transform to construct the
> analytic signal and downconvert it to baseband. Otherwise, I can get the
> signal multiplied by a sine and a cosine which oscillate at IF carrier
> frequency and then lowpass-filter unwanted parts. These two methods now
> also deal with complex numbers.
>
> What is the difference between these two methods?

As long as you can separate the mirror images, both methods are equvalent.

> I can't tell which is superior.

You have to use Hilbert transform if the image spectrum overlaps with
the downconverted spectrum.

DSP and Mixed Signal Design Consultant
http://www.abvolt.com
```
```On Sep 17, 2:52&#4294967295;am, "alomar" <alomar.w...@gmail.com> wrote:
> Hi, all
>
> I want to demodulate an IF real signal and it seems that there are some
> different methods on it. I can employ hilbert transform to construct the
> analytic signal and downconvert it to baseband. Otherwise, I can get the
> signal multiplied by a sine and a cosine which oscillate at IF carrier
> frequency and then lowpass-filter unwanted parts. These two methods now
> also deal with complex numbers.
>
> What is the difference between these two methods? I can't tell which is
> superior.
>

Maybe you will find this helpful:

http://www.claysturner.com/dsp/ASG.pdf

Clay

```
```>Hi, all
>
>I want to demodulate an IF real signal and it seems that there are some
>different methods on it. I can employ hilbert transform to construct the
>analytic signal and downconvert it to baseband. Otherwise, I can get the
>signal multiplied by a sine and a cosine which oscillate at IF carrier
>frequency and then lowpass-filter unwanted parts. These two methods now
>also deal with complex numbers.
>
>What is the difference between these two methods? I can't tell which is
>superior.
>
>
>

If you multiply by a sine and a cosine which oscillate at IF carrier
frequency you loss phase information. If you dont need thats information
you can use that method. Otherwise, you need hilbert transform.
```
```>>Hi, all
>>
>>I want to demodulate an IF real signal and it seems that there are some
>>different methods on it. I can employ hilbert transform to construct
the
>>analytic signal and downconvert it to baseband. Otherwise, I can get
the
>>signal multiplied by a sine and a cosine which oscillate at IF carrier
>>frequency and then lowpass-filter unwanted parts. These two methods now
>>also deal with complex numbers.
>>
>>What is the difference between these two methods? I can't tell which is
>>superior.
>>
>>
>>
>
>If you multiply by a sine and a cosine which oscillate at IF carrier
>frequency you loss phase information. If you dont need thats information
>you can use that method. Otherwise, you need hilbert transform.
>

```
```On 9/17/2009 5:07 PM, JAlbertoDJ wrote:
>> Hi, all
>>
>> I want to demodulate an IF real signal and it seems that there are some
>> different methods on it. I can employ hilbert transform to construct the
>> analytic signal and downconvert it to baseband. Otherwise, I can get the
>> signal multiplied by a sine and a cosine which oscillate at IF carrier
>> frequency and then lowpass-filter unwanted parts. These two methods now
>> also deal with complex numbers.
>>
>> What is the difference between these two methods? I can't tell which is
>> superior.
>>
>>
>>
>
> If you multiply by a sine and a cosine which oscillate at IF carrier
> frequency you loss phase information. If you dont need thats information
> you can use that method. Otherwise, you need hilbert transform.

How so?   PSK modems, where the information is in the phase, use
quadrature mixing for up and downconversion routinely.

--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com
```
```JAlbertoDJ wrote:
>> Hi, all
>>
>> I want to demodulate an IF real signal and it seems that there are some
>> different methods on it. I can employ hilbert transform to construct the
>> analytic signal and downconvert it to baseband. Otherwise, I can get the
>> signal multiplied by a sine and a cosine which oscillate at IF carrier
>> frequency and then lowpass-filter unwanted parts. These two methods now
>> also deal with complex numbers.
>>
>> What is the difference between these two methods? I can't tell which is
>> superior.

...

> If you multiply by a sine and a cosine which oscillate at IF carrier
> frequency you loss phase information.

Did Horus, the god of mathematics, tell you that? According to the math
I know, phase is preserved.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```>JAlbertoDJ wrote:
>>> Hi, all
>>>
>>> I want to demodulate an IF real signal and it seems that there are
some
>>> different methods on it. I can employ hilbert transform to construct
the
>>> analytic signal and downconvert it to baseband. Otherwise, I can get
the
>>> signal multiplied by a sine and a cosine which oscillate at IF
carrier
>>> frequency and then lowpass-filter unwanted parts. These two methods
now
>>> also deal with complex numbers.
>>>
>>> What is the difference between these two methods? I can't tell which
is
>>> superior.
>
>   ...
>
>> If you multiply by a sine and a cosine which oscillate at IF carrier
>> frequency you loss phase information.
>
>Did Horus, the god of mathematics, tell you that? According to the math
>I know, phase is preserved.
>
>   ...
>
>Jerry
>--
>Engineering is the art of making what you want from things you can get.
>&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;
>

I have wrote that because multiplying by a sine and a cosine i cannot do
run an Automatic Frecuency Control for my modem using atan(Im/Re) in the
FFT output.

Otherwise, with Hilbert transform instead of multiplying, AFC run
perfectly. why? i dont know, and i would like something explain to me.

In the example of PSK demodulation you dont have any problem with phase.
But....try to apply an AFC to your PSK demodulator and then tell me if
converge.

```
```On 9/18/2009 4:18 PM, JAlbertoDJ wrote:
>> JAlbertoDJ wrote:
>>>> Hi, all
>>>>
>>>> I want to demodulate an IF real signal and it seems that there are
> some
>>>> different methods on it. I can employ hilbert transform to construct
> the
>>>> analytic signal and downconvert it to baseband. Otherwise, I can get
> the
>>>> signal multiplied by a sine and a cosine which oscillate at IF
> carrier
>>>> frequency and then lowpass-filter unwanted parts. These two methods
> now
>>>> also deal with complex numbers.
>>>>
>>>> What is the difference between these two methods? I can't tell which
> is
>>>> superior.
>>    ...
>>
>>> If you multiply by a sine and a cosine which oscillate at IF carrier
>>> frequency you loss phase information.
>> Did Horus, the god of mathematics, tell you that? According to the math
>> I know, phase is preserved.
>>
>>    ...
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>> &#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;
>>
>
> I have wrote that because multiplying by a sine and a cosine i cannot do
> run an Automatic Frecuency Control for my modem using atan(Im/Re) in the
> FFT output.
>
> Otherwise, with Hilbert transform instead of multiplying, AFC run
> perfectly. why? i dont know, and i would like something explain to me.
>
> In the example of PSK demodulation you dont have any problem with phase.
> But....try to apply an AFC to your PSK demodulator and then tell me if
> converge.

Yes, the AFC will converge, as will a loop locked onto the carrier phase.

--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com
```