I'm working in signal processing and I would like to build a function f(t) (t is time) defined on R+, bounded on [a,b], derivable and which verifies Probability(f(t) is in [c,d])=(d-c), [c,d] being included in [a,b]. in other words, I would like a function that meets each point of [a,b] with the same probability, If I express it correctly.
An additional constraint on f would be that its frequential spectrum (with a given sampling frequency fe) does not contain values above a given value w. Thus, f is smoothed is a sense:
The idea I'm currently trying is to get uniform values between a and b at a rate w, then interpolate between the points to reach a sampling frequency fe. I'm not completely satisfied because the final curve reaches extreme values less frequently than central values (its distribution is a mode, I would like it to be flat). Have you got some ideas or isn't it clear ? Thanks in advance,