PDF of an impulse function?

What is the PDF (probability density function) of an impulse function?

Thanks in advance for your help.
Regards,
Theo (ntvdmlREMOVE@iafrica.com)

On 14 Aug 2003, Theo van der Merwe wrote:

> What is the PDF (probability density function) of an impulse function?
>
> Thanks in advance for your help.
> Regards,
> Theo (ntvdmlREMOVE@iafrica.com)
>

theo, i think you're looking for the definition of the PDP -- Power Delay
Profile.  the cumulative function gives you Pr( |h(t)| <= X ), where t is
the parameter.  note the absolute value sign.

do a google search on it, i'm sure you'll find plenty of examples.

julius

-- 
The most rigorous proofs will be shown by vigorous handwaving.
http://www.mit.edu/~kusuma

opinion of author is not necessarily of the institute

ntvdml@iafrica.com (Theo van der Merwe) wrote in message news:<25af4009.0308132304.4b651162@posting.google.com>...
> What is the PDF (probability density function) of an impulse function?
> 
> Thanks in advance for your help.
> Regards,
> Theo (ntvdmlREMOVE@iafrica.com)

Assuming that the magnitude of all impulses are same. And that the
data set only includes impulses and zeros, then calculate the no of
impulses and divide with total number of samples and same goes for
zeros. Take zero and magnitude as x-axis and there is your pdf of an
impulse train.

Vimal

"Theo van der Merwe" <ntvdml@iafrica.com> wrote in message
news:25af4009.0308132304.4b651162@posting.google.com...
> What is the PDF (probability density function) of an impulse function?
>
> Thanks in advance for your help.
> Regards,
> Theo (ntvdmlREMOVE@iafrica.com)

Theo,

Interesting question.  It makes one wonder "why"? you'd be asking it.
The impulse response is generally deterministic - unless it's measured
rather than calculated.
Even then, it may be rather deterministic.
So, what is the significance of its statistics if it is well defined?

I'm not suggesting anything - just curious.

Fred

ntvdml@iafrica.com (Theo van der Merwe) wrote in message news:<25af4009.0308132304.4b651162@posting.google.com>...
> What is the PDF (probability density function) of an impulse function?
> 
> Thanks in advance for your help.
> Regards,
> Theo (ntvdmlREMOVE@iafrica.com)

I don't understand the question.

This is the same as asking for the probability density function of the
function y = x^2.

mgodavarti@ditechcom.com (Mahesh Godavarti) wrote in message news:<d4cb12a3.0308140926.416a2616@posting.google.com>...
> ntvdml@iafrica.com (Theo van der Merwe) wrote in message news:<25af4009.0308132304.4b651162@posting.google.com>...
> > What is the PDF (probability density function) of an impulse function?
> > 
> > Thanks in advance for your help.
> > Regards,
> > Theo (ntvdmlREMOVE@iafrica.com)
> 
> I don't understand the question.
> 
> This is the same as asking for the probability density function of the
> function y = x^2.

Mahesh,

I don't see any problem of asking the above question. Let me explain a
bit.
Fred has rightly commented that for deteministics/defined/known
variable/signal it is not required to search for a  PDF or bang on its
statistics. For example, if x=constant, for any number of observations
it is always fixed at that point i.e the frequency of accumulating x
at points other than that constant is zero  so the PDF is a vertical
straight line and its height is proportional to the number of
observations.  We are rather interested to observe a random variable
in a defined interval. If the cumulative distibution function of a
random variable is
F(x) then PDF is defined as
f(x)=F(x)/dx. (F(x) has to be differetiable). Probability of observing
x in the
interval x to x+dx is f(x)dx, Graphically it covers the area bounded
by dx.

Now, if there is another variable such that, y=y(x) i.e your example,
then PDF of y is written as,

g(y)=f(x)/abs(dy/dx), where abs is absolute value.

similarly, it is possible to define mutidimensional PDF using Jacobi's
matrix.

santosh.nath@ntlworld.com (santosh nath) wrote in message news:<6afd943a.0308141423.42f948b9@posting.google.com>...

Santosh, there's a huge difference between "what is the PDF of y if y
= x^2" and "what is the PDF of the function y = x^2".

If he was asking the first question. That is, what is the pdf of y if
y = delta(x - xo) then the answer is f(y) = delta(y) as long
as Prob(x = x0) = 0.

If Prob(x = x0) > 0 then pdf of y is undefined.

mgodavarti@ditechcom.com (Mahesh Godavarti) wrote in message news:<d4cb12a3.0308142106.302f442@posting.google.com>...
> santosh.nath@ntlworld.com (santosh nath) wrote in message news:<6afd943a.0308141423.42f948b9@posting.google.com>...
> 
> Santosh, there's a huge difference between "what is the PDF of y if y
> = x^2" and "what is the PDF of the function y = x^2".
> 
> If he was asking the first question. That is, what is the pdf of y if
> y = delta(x - xo) then the answer is f(y) = delta(y) as long
> as Prob(x = x0) = 0.
> 
> If Prob(x = x0) > 0 then pdf of y is undefined.

I think you are putting me in confusion or I need to re-learn
mathematics.
I guess any function can be related with a variable i.e  if f(x) is a
function,
where x is another variable(could be dependent or independent)-let us
take for simplicity x is an independent varibale,

and y=f(x).
then I do not see any difference of PDF between y and f(x) and surely,
f(x) is
a function.

If you meant the above difference then I like to know or ask for a
proof from
you - otherwise I beg your pardon to understand you wrongly.

Regards,
Santosh

santosh.nath@ntlworld.com (santosh nath) wrote in message news:<6afd943a.0308150143.aea647@posting.google.com>...

Suppose your "job" is to count the number of balls in basket A and
place the square of the number of balls in basket B.

Then the difference I was talking about is similar to the difference
between the following two statements.

1) What is the pdf of the number of balls in basket B given the pdf of
number of balls in basket A?

2) What is the pdf of the "job"?

mgodavarti@ditechcom.com (Mahesh Godavarti) wrote in message news:<d4cb12a3.0308150836.2cf45812@posting.google.com>...
> santosh.nath@ntlworld.com (santosh nath) wrote in message news:<6afd943a.0308150143.aea647@posting.google.com>...
> 
> Suppose your "job" is to count the number of balls in basket A and
> place the square of the number of balls in basket B.
> 
> Then the difference I was talking about is similar to the difference
> between the following two statements.
> 
> 1) What is the pdf of the number of balls in basket B given the pdf of
> number of balls in basket A?
> 
> 2) What is the pdf of the "job"?

I am sorry to reject the second job-meaning the second statement
carries little meaning in  our statistics. It looks like "job" is well
defined and "and" specifies no toss to be done in the consequitive
tasks i.e PDF is not needed for the "job".

If instead of "and" you put "or" then obviously it has to specify a
separate PDF
for "job".
I guess I meant for the first one and it is already
discussed how to get the PDF.
Could the original poster clarify what he acually meant -the first one
or second one?