一个数字频谱转换成另一种 [英] Convert one number spectrum into another

问题描述

我试图想出一个公式推它把一个数字谱成另一种。 例如：

I'm trying to come up with a formular which converts one number spectrum into another. For example:

0 - 800 到 -1 - 1

其中， 0 = -1 ， 200 = -0.5 ， 400 = 0 ， 600 = 0.5 ， 800 = 1 ，等等。

Where 0 = -1, 200 = -0.5, 400 = 0, 600 = 0.5, 800 = 1, and so on.

困难的部分对我来说似乎是负的范围内。

The difficult part for me seems to be the negative range.

推荐答案

如果你的范围是 A0，A1 和 B0，B1 ，那么想要 X 去

If your ranges are a0, a1 and b0, b1, then you want x to go to

((x-a0)/(a1-a0)) * (b1-b0) + b0

基本上，（X-A0）是如何远远超过了你是从第一个范围的下侧，而（X-A0） /（A1-A0）除以范围的宽度，这样的数量是现在归 [0,1] 。在那之后，我们乘以（B1-B0）扩大范围到新的规模，并添加 B0 来转移过来。

Basically, (x-a0) is how far over you are from the lower side of the first range, and (x-a0)/(a1-a0) divides by the width of the range so the number is now normalized to [0, 1]. After that, we multiply by (b1-b0) to expand the range to the new scale, and add b0 to shift it over.

例如：

>>> a0, a1 = 0.0, 800.0
>>> b0, b1 = -1.0, 1.0
>>> 
>>> x = 400 # should go to 0
>>> x-a0
400.0
>>> (x-a0)/(a1-a0)
0.5
>>> (x-a0)/(a1-a0) * (b1-b0)
1.0
>>> (x-a0)/(a1-a0) * (b1-b0) + b0
0.0
>>> x = 0 # should go to -1
>>> (x-a0)/(a1-a0) * (b1-b0) + b0
-1.0
>>> x = 800 # should go to 1
>>> (x-a0)/(a1-a0) * (b1-b0) + b0
1.0

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