Re: Creating White Noise in Matlab
- From: illywhacker <illywacker@xxxxxxxxx>
- Date: Wed, 21 May 2008 12:46:45 -0700 (PDT)
On May 5, 6:51 pm, miki <miki.li...@xxxxxxxxx> wrote:
Hello All,
How can I generate a Gaussian white noise process in Matlab?
To be more specefic, I want to generate the process x(t)=w(t) where
E[w(t)] = 0
E[w(t)w(s)] = (Q*Q)*dirac(t-s)
Well, In matlab (in discrete form), If (t_(k+1) - t_k) = dt < 1
then one might think that x_t_k = Q*randn is the white noise.
But, I dont think so. something is missing here that should include
the discrete sampling dt.
For example, in order to solve the random walk equation
x_dot = w(t)
then x_t_(k+1) = x_t_k + Q*sqrt(dt)*randn is the correct solution.
BECAUSE THERE IS NO WHITE NOISE (as defined above) IN DISCRETE SPACE.
So what is the correct form of just white noise process in Matlab as I
asked in the beginning of the question.
Thanks in advance,
Miki
Clearly you cannot generate elements of the continuous time process,
as they are functions on R. You can generate coarser resolution
versions, though, in a principled way, by discretization. Define a
discrete time process to be the projection of the continuous time
process by a linear operator that takes averages over small, disjoint
time periods. You can derive the covariance (the mean is obviously
zero) of this process, which remains Gaussian with the value at each
discrete time independent of the others. This is the best you can do.
Note that the expectation of any quantity that only depends on the
coarse resolution function is the same under both processes.
illywhacker;
.
- References:
- Creating White Noise in Matlab
- From: miki
- Creating White Noise in Matlab
- Prev by Date: Re: How to Become a Pure Mathematician (or Statistician): Now with a Blog
- Next by Date: Re: Mean/ Median
- Previous by thread: Re: Creating White Noise in Matlab
- Next by thread: principal component regression
- Index(es):
Relevant Pages
|
