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Re: explaining i/q

From: Aditya Arun Kumar
Subject: Re: explaining i/q
Date: Tue, 3 Nov 2020 06:01:01 +0530

Visualizing IQ may help you a lot, while I was referring I referred to this material, http://dspguru.com/files/QuadSignals.pdf. Apart from that, I have a personal blog where I have explained some of the concepts of a complex number and its involvement in IQ (https://bpcu.blogspot.com/2020/10/understanding-iq-in-communication.html). I have one more of these coming out with respect to quad signals, I'll attach the source code of that here so, that you may take a look.

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On Tue, Nov 3, 2020 at 4:33 AM Kristoff <kristoff@skypro.be> wrote:
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:

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

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! :-)

kristoff - ON1ARF

S. Aditya Arun Kumar
Security Researcher, Comms

Attachment: IQ_vis.ipynb
Description: Binary data

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