# Hilbert Transform Problem

Started by April 30, 2009
```Dear All,
I have a question regarding hilbert transformer. If i take the
bandpass signal and sample it it would be real. Now when i multiply it
with a complex exponential to downconvert it I get a complex baseband
signal. On the other hand, if i take the bandpass signal, pass it
through a hilbert transformer and get a complex signal, and then
downconvert using complex multiplication i get different baseband
data. Why is it so as in both cases I am multiplying with a complex
exponential. In summary, what is the difference between these two
methods of downconversion.
i). multiplying real data with complex exponential -> complex output
ii). multiplying complex passband data with complex exponential ->
complex output

aitezaz
```
```On May 1, 2:44&#2013266080;am, aitezaz....@gmail.com wrote:
> Dear All,
> I have a question regarding hilbert transformer. If i take the
> bandpass signal and sample it it would be real. Now when i multiply it
> with a complex exponential to downconvert it I get a complex baseband
> signal. On the other hand, if i take the bandpass signal, pass it
> through a hilbert transformer and get a complex signal, and then
> downconvert using complex multiplication i get different baseband
> data. Why is it so as in both cases I am multiplying with a complex
> exponential. In summary, what is the difference between these two
> methods of downconversion.
> i). multiplying real data with complex exponential -> complex output
> ii). multiplying complex passband data with complex exponential ->
> complex output
>
> aitezaz

Ok - Hilbert transformers are delicate. Did you handle it properly?
Sometimes the windings on the secondary can come off.

Hardy
```
```On Apr 30, 10:44&#2013266080;am, aitezaz....@gmail.com wrote:
> Dear All,
> I have a question regarding hilbert transformer. If i take the
> bandpass signal and sample it it would be real. Now when i multiply it
> with a complex exponential to downconvert it I get a complex baseband
> signal. On the other hand, if i take the bandpass signal, pass it
> through a hilbert transformer and get a complex signal, and then
> downconvert using complex multiplication i get different baseband
> data. Why is it so as in both cases I am multiplying with a complex
> exponential. In summary, what is the difference between these two
> methods of downconversion.
> i). multiplying real data with complex exponential -> complex output
> ii). multiplying complex passband data with complex exponential ->
> complex output
>
> aitezaz

Case i) will contain baseband plus an image. Case ii) will not.

John
```
```On Apr 30, 12:06&#2013266080;pm, John <sampson...@gmail.com> wrote:
> On Apr 30, 10:44&#2013266080;am, aitezaz....@gmail.com wrote:
>
> > Dear All,
> > I have a question regarding hilbert transformer. If i take the
> > bandpass signal and sample it it would be real. Now when i multiply it
> > with a complex exponential to downconvert it I get a complex baseband
> > signal. On the other hand, if i take the bandpass signal, pass it
> > through a hilbert transformer and get a complex signal, and then
> > downconvert using complex multiplication i get different baseband
> > data. Why is it so as in both cases I am multiplying with a complex
> > exponential. In summary, what is the difference between these two
> > methods of downconversion.
> > i). multiplying real data with complex exponential -> complex output
> > ii). multiplying complex passband data with complex exponential ->
> > complex output
>
> > aitezaz
>
> Case i) will contain baseband plus an image. Case ii) will not.
>
> John

Thanks john!
i got it right.... and if i want to make these two cases the same,
should i LPF filter the I and Q channels in case i). And i will get
the same output ?

aitezaz
```
```On May 1, 9:37&#2013266080;am, aitezaz....@gmail.com wrote:
> On Apr 30, 12:06&#2013266080;pm, John <sampson...@gmail.com> wrote:
>
>
>
> > On Apr 30, 10:44&#2013266080;am, aitezaz....@gmail.com wrote:
>
> > > Dear All,
> > > I have a question regarding hilbert transformer. If i take the
> > > bandpass signal and sample it it would be real. Now when i multiply it
> > > with a complex exponential to downconvert it I get a complex baseband
> > > signal. On the other hand, if i take the bandpass signal, pass it
> > > through a hilbert transformer and get a complex signal, and then
> > > downconvert using complex multiplication i get different baseband
> > > data. Why is it so as in both cases I am multiplying with a complex
> > > exponential. In summary, what is the difference between these two
> > > methods of downconversion.
> > > i). multiplying real data with complex exponential -> complex output
> > > ii). multiplying complex passband data with complex exponential ->
> > > complex output
>
> > > aitezaz
>
> > Case i) will contain baseband plus an image. Case ii) will not.
>
> > John
>
> Thanks john!
> i got it right.... and if i want to make these two cases the same,
> should i LPF filter the I and Q channels in case i). And i will get
> the same output ?
>
> aitezaz

It should be close.

John
```