From the Equation OCR front line…

##### Problem:

Splitting up handwritten calculations into single lines.* *

##### Algorithm description:

First map all the strokes on the y-axis. Then travel along the axis and record the the *ink density* (number of strokes underneath). Remember local maximums. If the density falls below a certain percentage (tolerance) of a last local maximum – insert a break line.

##### C# code:

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As promised last week I’m going to compare three methods of optimizing 2 ^ x calculation:

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Signal processing often requires moving between logarithmic & linear domains. In audio area we can talk about Octaves (logarithmic representation) and Frequencies (linear representation). Octave -> Frequency conversion corresponds to transformation** x = 2 ^ x**.

Most programming languages provide support for such calculation, for example Pow(a, b) in C#.

Those functions however tend to be time consuming. We can take advantage of the fact that in our case *a = const = 2* and optimize the calculation.

Let’s start with equation:

###### a ^ ( b + c ) = a ^ b * a ^ c

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