# Calculating chirp of a discrete signal

In the paper, The averaging method for finding exactly periodic dispersion-managed solitons , there is an expression for the chirp $$C$$ of a signal given by-

$$C = \frac{\text{Im}\int_{-\infty}^{\infty} u^2u_t^2 dt}{|u|^4dt}$$

I am writing a program to calculate the chirp on MATLAB. The chirp function I have written so far is-

function c = chirp(signal)
u = signal;

• I lack access to the paper, so I will work with what I can see. (1) Since this involves the evolution of solitons, I assume that $u$ is a function of both space ($x$ or $\mathbf{x}$) and time ($t$). The integral in the numerator involves the time-derivative, but your code uses what I assume is a space derivative (gradient). (2) Does using a more sophisticated numerical integration method (say, trapz) for the integrals yield any improvement? – Joe Mack Sep 16 at 21:02