Real vs. Complex

Started by February 26, 2007
```I have a question about real and complex numbers.  I want to plot the
phase and magnitude of a signal that will chirp in frequency from
10MHz to 30MHz.  I really want to do more than this, but I think this
can easily explain my problem.  This can be done in Matlab with no
problem, using a complex signal.  However in the real world I don't
have a complex value, just a real value sampled from an A/D.  Is there
anyway I can create a complex value from this signal by oversampling?
I know there are techniques to do this if I sample at four times the
input frequency, but the input frequency is changing so I don't think
I can use those techniques.  I have also tried mixing the real signal
with a complex signal created in Matlab and this gets me close, but is
could give me.

```
```birdforsale@gmail.com wrote:
> I have a question about real and complex numbers.  I want to plot the
> phase and magnitude of a signal that will chirp in frequency from
> 10MHz to 30MHz.  I really want to do more than this, but I think this
> can easily explain my problem.  This can be done in Matlab with no
> problem, using a complex signal.  However in the real world I don't
> have a complex value, just a real value sampled from an A/D.  Is there
> anyway I can create a complex value from this signal by oversampling?
> I know there are techniques to do this if I sample at four times the
> input frequency, but the input frequency is changing so I don't think
> I can use those techniques.  I have also tried mixing the real signal
> with a complex signal created in Matlab and this gets me close, but is
> could give me.
>
Look up Hilbert transform. Sample twice as fast as you would with a
complex signal, and use a Hilbert transform to create a quadrature
signal. Now you have a complex signal at twice the sampling rate of your
original complex signal. Complex decimation to get exactly back to your
naturally complex signal is possible.

Steve
```
```> I have a question about real and complex numbers.  I want to plot the
> phase and magnitude of a signal that will chirp in frequency from
> 10MHz to 30MHz.
...
> Is there anyway I can create a complex value from this signal ... ?

You can try the Matlab 'hilbert' function to create a complex signal.
This contains the 'instantaneous' magnitude and phase of your signal.
To look at the phase, use the 'unwrap' function.

Regards,
Andor

```