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.
https://wirelesspi.com/i-q-signals-101-neither-complex-nor-complicated
Cheers,
Qasim
From: Kristoff <krist...@skypro.be>
To: discuss-gnuradio@gnu.org
Subject: Re: explaining i/q
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
