Here’s a YouTube video that’s got a bit of pencil math (so it doesn’t drone on) 
and oscilloscopes (for the ham guys), so it’s got a bit for everyone .

https://m.youtube.com/watch?list=PLvOgjCaG0WzDAF1Um894vv95mrcyortOB&v=h_7d-m1ehoY

> On Nov 4, 2020, at 7:52 AM, Kristoff <krist...@skypro.be> wrote:
> 
> Jef,
> 
> 
> Concerning the term "slope". Well, I also have my doubts about it. I think 
> that for a lot of people, this would create the assumption that the signal 
> then goes from the 'i' value to the 'q' value in a straight line, which is 
> -as we know- not the case.
> 
> Sometimes it helps to -at first- give a very basic mental image of something, 
> and -at the end, when people understand the topic- "correct" that image with 
> a more correct one, or just point them to some youtube video that explains 
> the topic in more detail.
> 
> 
> Anycase,this is indeed all an interesting exercise in braking down concepts 
> into very small steps.
> 
> The amateur-radio community is a bit strange as most people do have a 
> technical background, but for a large number of hams, that is mainly based on 
> assumptions or "that's what they said in the ham-radio courses", without 
> understanding the full technical details, especially topics that are highly 
> based on math.
> For most hams, "SDR" is just "that piece of software you install on your 
> computer to look at  waterfall graphs".
> 
> So we have a very long way to go. :-)
> 
> 
> 73
> kristoff - ON1ARF
> 
> 
> 
>> On 4/11/2020 02:21, Jeff Long wrote:
>> It's more important to give people some mental picture than to make sure 
>> it's completely correct. But, I would not use the "slope" terminology. The 
>> important things are, as you've said, (1) with the complex type, you can 
>> have a signal at baseband that is not symmetric, and (2) the price for this 
>> is doubling the amount of data needed. The signal you deal with at baseband 
>> is the same signal that is seen centered on the RF carrier.
>> 
>> I don't see a great way to talk about "phase" without going into the math. 
>> It is important to get into "phase" when you talk about any modulation 
>> fancier than slow FSK.
>> 
>> Good luck. Hope you find the right balance between useful, digestible, and 
>> correct.
>> 
>> On Tue, Nov 3, 2020 at 7:20 PM David Hagood <david.hag...@gmail.com 
>> <mailto:david.hag...@gmail.com>> wrote:
>> 
>>    I am sorrowful that you have decided you are going to stick with an
>>    explanation that is fundamentally incorrect. I know how direct
>>    conversion systems work - I design the software for them for a
>>    living.
>>    What you are basing your mental model on is an optimization for
>>    the case
>>    where the system is both sub-sampling the signal and going digital in
>>    the same operation. However, in many extremely high sample rate
>>    systems,
>>    the signal is brought down to baseband by mixing it with analog
>>    quadrature signals - that's the place where I and Q come from - and I
>>    assure you the only "delay by 90 degrees" is in the creation of the
>>    quadrature LO signals, not in the sampling of the actual data. But
>>    I've
>>    been around the Sun enough times to know that since you have decided
>>    upon this course and don't seem to want to change, there's no
>>    point in
>>    continuing to try to help.
>> 
>> 
> 
> 

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