I have a deterministic signal comming from an experiment:

x1[n]=[2,3,2,4,1,4] as a set={1,2,3,4} histogram={1/6,2/6,1/6,2/6}

what does the histogram(number of occurrence of each value) mean in the case of a deterministic signal such as X1[n]? It's not the probability density function, since we don't define a probability density function for a deterministic signal.

Thanks for any clarification

  • $\begingroup$ It all depends on how you think about it. Somebody sampling independently with replacement from the multiset $(2,3,2,4,1,4)$ would indeed equate your "histogram" (actually, relative frequencies) with a probability distribution. Thus, to answer your question it would help us to know how you intend to use this frequency information. $\endgroup$
    – whuber
    Oct 25 '12 at 13:29
  • $\begingroup$ i don't get your point.either this deterministic signal will occur(it's a deterministic signal of a random process) during one test or not. if it occurs,it means that all those above points will happen as well.so the probability of these points happening is the same as the probability that this deterministic signal happens in my random process.am i right? $\endgroup$
    – Michelle
    Oct 25 '12 at 13:53
  • $\begingroup$ You seem now to be asking a question about a multivariate distribution, but it's not clear what you're trying to find out (at least not to me). Your use of "deterministic signal" in the same breath with "random process" looks self-contradictory to me, too. Is there any way you could edit the question to clear up these ambiguities about what you're referring to and what you are trying to find out? $\endgroup$
    – whuber
    Oct 25 '12 at 13:57
  • $\begingroup$ Hi again.first of all let me say that I'm a new graduate. A random process is composed of several deterministic signals.it's called Random processwe don't know which one of these deterministic signals will happen in a trial. $\endgroup$
    – Michelle
    Oct 25 '12 at 14:06
  • $\begingroup$ OK, that clears up one item. (To avoid potential confusion about using "deterministic" and "stochastic" for the same thing, people often say you have one realization or path of that stochastic process.) Notice that your frequency vector summarizes this realization, and thereby strips away all time information. Whether this is meaningful or not depends on what you plan on doing with these frequencies. Are you perhaps reading something in which those frequencies are computed and used? Do you have a reference? $\endgroup$
    – whuber
    Oct 25 '12 at 14:11

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