Hi everyone
Hope you're doing well. Someone pointed me towards this discussion on the mailing list and I thought that it's a great topic to explain without complex numbers, phasors, orthogonality, etc. So I wrote about it for a true beginner.
Instead of focusing on a small length, my main purpose was to produce some beautiful figures that can help one grasp why both I and Q samples are required.
Cheers,
Qasim
Hi all,
I was watching the webinar of Heather on GNU Radio today, when it came
to me that one of the most difficult part doing a presentation of GNU
Radio is the data-types, .. and especially these 'complex numbers'.
The problem, or at least for me, is that when you mention 'GNU Radio
complex numbers', you also have to mention iq-signals, which is a topic
that is very difficult to explain in 10 seconds to an audience who has
never seen anything about i/q sampling before.
I have been thinking on how to explain the concept of I/Q signalling in
just a few lines, e.g. in the context of -say- a workshop on GR.
I have this idea in my head:
Statement:
The main difference between sampling with reals ('floats') and i/q
sampling with complex numbers, is that the latter does not only provide
the instantaneous value (voltage) of a signal at a certain point of
time, but also includes phase information (i.e. the slope of the signal
at that point).
To make this visual:
Take half a sine-wave and plot it out for every 45 degrees.
This gives you 5 points: 0 (0 degrees), sqrt(2)/2 (45 degrees), 1 (90
degrees), sqrt(2)/2 (135 degrees) and 0 (180 degrees).
Now look at the 2nd and the 4th point (45 degrees and 135 degrees), if
you sample this using only real/float values, these two points are
exactly the same (sqrt(2)/2). Just based on these values by themselves
(i.e. remove all other points from the graph), there is no way you can
tell that at the first point (45 degrees) the graph was going up, while
at the 135-degrees point the graph was going down.
So, ... what i/q sampling does, is for every point "x", it not only
provide the value of the graph at that point of time, but also
information of the slope of the graphs at that time.
This also explains while i/q sampling is done by not just taking the
value of a signal at point "t", but also at 1/4 period later (which is
the information you need to determine the 'slope' of that graph at point
't')
So, ... is this statement correct?
If it is more-or-less correct and it can help provide a basic mental
image of the concept of i/q sampling, I would be more then happy! :-)
73
kristoff - ON1ARF