From linear to logarithmic distribution
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Given a linear frequency scale denoted by the vector f = 1:fmax; fmax is known, say 1000.
How can I construct, out of this vector, a logarithmic selection of the entries such that the ratio between two consecutive odd numbers is 1.1?
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Walter Roberson
il 9 Giu 2015
You cannot. The only solution to x*11/10 = x+2 is x = 20, and that is an even number.
If the task is to construct a vector of length fmax such that the ratio
x(2*k+3)/x(2*k+1)
is 11/10 for k in nonnegative integers, then as logarithmic progression is x(n+1) = C * x(n) for some constant C, it follows that x(n+2) = C*(C*x(n)) = C^2 * x(n). You want that value, C^2 to be 1.1, so your C is sqrt(1.1). Then you get
initial_value * sqrt(1.1).^(0:fmax-1)
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Walter Roberson
il 10 Giu 2015
I have no idea what that code is intended to do. It is uncommented and the relationship to the Question you posted is not obvious.
You start with Lines=1 which is length 1. In the first statement in your while you try to index Lines from 2 to length(Lines_linear) which would be 2:500. But Lines only has 1 entry, so you cannot access elements 2 to 500 of it.
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