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June 13th, 2012, 02:17 AM   #1
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Going insane over range conversion

First of all, hello forum! hope you're having a good day

Turns out I'm as acknowledgeable in math as anyone who barely finished high school back in 1981 and never quite did any relevant math ever since...Very unfortunate but that's the way it is. My field of work doesn't call for anything related to numbers so I've pretty much forgotten everything I ever learned. With that in mind, I'm hoping you won't be offended by my display of stupidity, my embarrassing inability to comprehend something that must not be any more complicated than 1+1 for the lot of you. I must also apologize beforehand since it's very likely that this post may end up in the wrong section of the forum.

Without further ado, my problem:

I need to convert a couple of numbers between two ranges. The range I'm converting from goes from -0.538 to +0.538. The numbers I need to convert are -0.31146 and +0.298.

The range I'm converting to goes from -255 to +255, but the "midpoint" or the very specific number where the signal is perfectly balanced isn't "0" but +67! This I've been told to take into account.

Well, that's pretty much it. Looks like nothing but I'm clueless as clueless gets. I need an answer and more importantly, a formula that I can use to perform similar conversions.

Very much appreciated.

Yours truly,
Michelle.
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June 13th, 2012, 05:46 AM   #2
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Re: Going insane over range conversion

It looks like you don't have enough information to do this with great accuracy. All that you know is that "neutral" (presumably 0.0) must be turned into +67, but this could be interpreted as a broken line before and after, or as a smooth curve of some kind:

[attachment=0:qezqymbw]range.png[/attachment:qezqymbw]

The broken line is dark green, while the light blue curve is a parabola through the points.

Here are the results of two different methods of conversion:

-.31146
Broken line: -119.41
Parabola: -103.08

+0.298
Broken line: +171.13
Parabola: +187.69

What kind of signal conversion is it? That might help.
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File Type: png range.png (3.4 KB, 415 views)
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June 13th, 2012, 03:10 PM   #3
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Re: Going insane over range conversion

Thank you very much, aswoods. That really is all the information I have. The signal in question is a video signal (I'm doing a crash course on video engineering) and this is the second math problem that I've been presented, plus I was deliberately left uninformed about the uses of such operation.

It kind of is a way to test how much the students really know, so I'm guessing the kind of signal would be irrelevant to the problem since we haven't even advanced to that part of the course.

Do you think you could give me a moron-proof explanation on how you to create and interpret that parabola graphic? by that I mean, how exactly did you come up with the results. I really need to understand it down to the basics so I can use it in the future.

Best regards.
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June 13th, 2012, 06:24 PM   #4
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Re: Going insane over range conversion

You are converting from -.538 ... +.538 to -255 to +255, so the x axis is the old signal and the y axis is the new signal.

-.538 turns into -255 (bottom-left dot)
0.0 turns into +67 (middle dot)
+.538 turns into +255 (top-right dot)

Just ignore the smooth curve which I only gave as an example and use the broken line.

On the left-hand side, you must get from -.538 to 0.0 rightwards while going from -255 to +67 upwards.
So you travel .538 to the right, while travelling a distance of 255+67 = 322 up.
That means that for a small change in a negative old signal, there must be a change 322/.538 = 598.513 times the size in the new signal.
Say you start at the centre (0.0, +67). If the old signal goes down to -.31146, the change in the new signal must be 598.513 times as big, so it must go down .31146 * 598.513, starting from +67.
67 - .31146 * 598.513 = -119.413...

On the right-hand side, you must get from 0.0 to +.538 rightwards while going from +67 to +255 upwards.
So you travel .538 to the right, while travelling a distance of 255-67 = 188 up.
For a small change in a positive old signal, there must be a change 188/.538 = 349.442 times the size in the new signal.
Again start at (0,0, +67). If the old signal goes up to +0.298, the change in the new signal must be 349.442 times as big, so...
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