Bidirectional Logarithmic Compression - John Dunn, Consultant, Ambertec, P.E., P.C.

You can be confronted with some dependent variable that varies versus some independent variable where that variation just happens to be of the greatest interest when the independent variable is somewhere in the middle of a numerical range.

A graphic image of the relationship between the two variables may benefit if the x-axis of the presentation is given a bidirectional logarithmic compression along the lines (no pun intended) of the following examples.

Here, we look at x-axis plots of a variable from zero to 100 with the center value equaling 50. Vertical rises are shown upward at increments of 10:   

 
 

The larger you make the coefficient K2, the more expanded the x-axis becomes in the center and the more compressed at each end. Coefficient K1 then needs to be tailored for the appropriate width.

Comments

[John Dunn]

I should have mentioned that this presentation method came about from presenting some antenna radiation pattern data. The bidirectional compression made a side-lobe issue more readily visible.

[General contractor chicago]

Logarithmic compression was so hard to understand.