Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.stat.math.independent

Topic: Binomial variance for DFT
Replies: 1   Last Post: Dec 27, 2012 10:18 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David Jones

Posts: 62
Registered: 2/9/12
Re: Binomial variance for DFT
Posted: Dec 27, 2012 10:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



"Cristiano" wrote in message news:kbhdes$9f3$1@dont-email.me...

I have n/2 real numbers.

I calculate a threshold T (a real number) for which p * n/2 numbers (0 <
p < 1) are expected to fall below T.

Then I count how many numbers are less than T.

That count should have a binomial distribution, right? Hence, its
variance should be
n/2 * p * (1-p).

But the n/2 numbers are the modulus of the first n/2 complex numbers
obtained from a discrete Fourier transform and the variance should be
n/2 * p * (1-p) / 2
as explained here (page 10):
http://eprint.iacr.org/2004/018.pdf

Unfortunately, the value given in the paper is significantly different
from the one obtained by extensive simulations.

Does anybody now a procedure or a formula to calculate the exact
variance of the counts?

Thanks
Cristiano

-------------------------------------------------------------------------------

There seems very little "explanation" in the paper you cite.

However, you might like to start from the non-asymptotic theory of the
periodogram, such as given by Priestly (MB Priestly, 1981, "Spectral
Analysis and Time Series Analysis", Academic Press, Theorem 6.1.3 and
surrounding text). Things to consider are (i) the non-zero excess kurtosis
of the starting random variables in the test case: (ii) the correlation at
adjacent/neighbouring frequencies.





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.