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Topic: function of uniform probability
Replies: 4   Last Post: Feb 11, 2009 3:05 AM

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 Boris Posts: 13 Registered: 12/7/04
function of uniform probability
Posted: Feb 10, 2009 10:21 AM

Hi,

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 ?