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explaining i/q

From: Kristoff
Subject: explaining i/q
Date: Tue, 3 Nov 2020 00:02:29 +0100
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:68.0) Gecko/20100101 Thunderbird/68.10.0

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 theĀ  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! :-)

kristoff - ON1ARF

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