how to calculate lipschitz constant?

For a one-dimensional signal, in order to quantitatively characterize the singularity of each point, how to calculate the Lipschitz constants of each point?

Answer 1

[Aleksi Kristian Winstén]

Hi,

this answer comes a bit late, but I wish someone still finds this information usefull.

Lipschits constant is defined as

From the mean value theoream one can see that

so at every point if the constant Lis greater or equal than the norm of the functions derivative, then L is the Lipschitz constant.

The procedure to find the Lipschitz constant is to calculate the derivative of the function and then check if the derivative function is bounded by some value L on the domain - - that is your Lipschits constant.

Usually the norm is the euclidean-norm

You can do the calculations with symbolic toolbox

syms x
f = sin(x); % here we define the function
df = diff(f) % here we calculate the derivative function of sin(x)
df = abs(df) % here we use the euclidean norm
fplot(df) % plots the abs(df). The function is clearly limited with upper bound M=1
           % so the Lipschits constant is L >= 1