Re: I have a few questions about random processes ...
- From: "Fred Marshall" <fmarshallx@xxxxxxxxxxxxxxxxxxxx>
- Date: Sat, 8 Oct 2005 08:01:50 -0700
"comtech" <comtech.usa@xxxxxxxxx> wrote in message
news:1128757300.913454.30520@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hi all,
>
> I am trying to think conceptually about these questions... please help
> me! Thank you very much!
>
> 1. Is there such a random process called exponential process, similar
> to what is called the Gaussian process?
>
> 2. Can all probability distribution be generated from uniform
> distribution? (even non-invertible functions)?
>
> 3. Why people take the Foureir Transform of the autocorrelation
> function instead of the random process itself? What's the reasoning
> behind it?
>
> What's the relationship between the PSD fo random process(Fourier
> Transform of autocorrelation function) vs. the Fourier Transform of
> random process treated as a time function itself?
>
> 4. Gaussion process is a process that is completely determined by its
> first and second order statistics... is a process which is completely
> determined by its first and second order statistics a Gaussian process?
>
>
> What is the process which is completely determiend by its first order
> statistics?
>
> What is the process which is completely determined by its first, second
> and third statistics?
It seems obvious that you're not working on learning about one thing or
solving *a* problem. Maybe you can help us understand the context of your
questions - i.e. why are you asking? Or, more bluntly, this sounds way too
much like homework.
> 1. Is there such a random process called exponential process, similar
> to what is called the Gaussian process?
Close but no cigar. Google is your friend.
> 2. Can all probability distribution be generated from uniform
> distribution? (even non-invertible functions)?
No way - unless you define "generate" differently than I do or have
constraints that haven't been stated ... and you may well.
I normally think of the generation (or calculation) of probability density
functions as combinations of PDFs for things that are used or connected
together. For example, if I have a family of resistors that each have a
uniform distribution of their values within the tolerance range then what is
the PDF for 2 resistors in series? 3? etc.
The resulting PDF is the convolution of the PDFs of the individual
resistors.
So, 2 resistors yield a triangular PDF, etc. What about 2 resistors in
parallel?
Sometimes things have a bimodal PDF - it peaks at the edges and is zero in
the middle. For example, this is indicative of a distribution of culled
part values - the center valued parts have been removed because they
represent a population with better tolerance.
I see no way to "generate" the bimodal PDF from a single uniform
distribution.
I guess you could add two disjoint uniform PDFs together - but is that to
"generate"?
Maybe in "signals" these examples are off the chart....
> 3. Why people take the Foureir Transform of the autocorrelation
> function instead of the random process itself? What's the reasoning
> behind it?
>
Maybe they just like looking at the autocorrelation function... How many
samples will be transformed in each case? Does that suggest anything at
all? Or, maybe you mean an infinite continuous Fourier Transform?
Might it have anything to do with where the energy is concentrated between
the two? and thus, the length of the transform or integral that must be
computed?
What's the difference between:
1) Taking the FT of a random sequence and multiplying by its own complex
conjugate
and
2) Computing the autocorrelation function and taking the FT?
(over what time must the autocorrelation be computed? infinite?)
If the autocorrelation function is highly concentrated in time, what is the
nature of the energy distribution in frequency for its Fourier Transform?
> 4. Gaussion process is a process that is completely determined by its
> first and second order statistics... is a process which is completely
> determined by its first and second order statistics a Gaussian process?
>
>
> What is the process which is completely determiend by its first order
> statistics?
>
> What is the process which is completely determined by its first, second
> and third statistics?
What is *THE* process? Seems like we're getting away from "conceptual" here
and into semantics / definitions. Of course I may be missing something.
With all the cross-posts, I wonder if you'll ever get back to read this on
comp.dsp? :-(
Fred
.
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