```Date: Feb 10, 2009 8:52 PM
Author: matt271829-news@yahoo.co.uk
Subject: Re: function of uniform probability

On Feb 10, 3:21 pm, Boris Gourévitch <bo...@SUS-AU-SPAMpi314.net>wrote:> Hi,>Hi, I'm not entirely sure I understand your question, so if my replydoesn't make any sense then please ignore it.> 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], derivableI'm wondering if you might mean "differentiable" rather than"derivable"...> and which> verifies Probability(f(t) is in [c,d])=(d-c), [c,d] being included in> [a,b].Do you mean f(t) at a uniformly randomly chosen instant in time? I'mnot sure it's logically possible to choose such an instant unless youconstrain t to lie in a finite time interval -- though you cansidestep this issue by using a periodic function. Also, probability isa number between zero and one, so I'm wondering if you mean theprobability is *proportional* to d - c, rather than equal to it.I'm guessing that your probability requirements are such that asawtooth wave would work, except that's no good to you because it'snot smooth. I don't see that a smooth bounded periodic functiondefined for all t > 0 is possible: f(t) will inevitably be biasedtowards the points of maximum and minimum when arbitrarily smallintervals [c,d] are considered. For the same reason, I don't see thata smooth function defined over a finite timespan (with t chosenuniformly randomly from that timespan) will be possible either, exceptfor the trivial case of a linear function. The only way I can see isto somehow contrive to have a maximum or minimum at every value within[a,b] (for some t) and make the limiting probability over t = 0 to t =T come right as T -> infinity, if that's possible (I don't know if itis). But the probabilities wouldn't be right with t chosen from anyfinite time interval.> 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,>> Boris
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