I have discrete signals whose values are between 0 and 1.
I wish to post-process such a signal such that the mean of its values equals 0.5, yet keeping maximum and minimum values 0/1 intact. Intuitively, I think an 'element-wise' exponential would be the right approach, yet I can't seem to come up with the method to determine the value of the appropriate exponential.
Fictive matlab example to illustrate:
>> s=[0.2 0.7 1 0.5 0.4 0.2 0 0.3]; >> mu=mean(s) mu = 0.41250 >> s_adjusted=s.^0.69998; >> mu_adjusted=mean(s_adjusted) mu_adjusted = 0.50000
What is the best method to determine the 0.69998 exponential ?