Integration over log space

Approximates an integral with samples on a logarithmic scale

Approximates integrals of functions which are sampled over a logarithmic space.
The integration is accurate where the function Y is smooth (piece-wise linear) on a logarithmic scale. For such functions the integral may be evaluated accurately, using fewer samples in comparison to linear sampling. A natural application is integration of transfer functions, for which the frequency samples are usually logarithmically spaced.
Inputs:
X - vector of samples.
Y - corresponding function values. If Y is a matrix, each of its columns is integrated with respect to X.
Output:
int - integration result.
Written by Dr. Yoash Levron, Dec. 2015