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Science Forum Index » Statistics - Math Forum » Creating White Noise in Matlab...
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| miki... |
 Posted: Mon May 05, 2008 6:51 am |
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Guest
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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 |
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| Herman Rubin... |
| Posted: Mon May 05, 2008 9:06 pm |
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In article <c420f084-23f9-4c3e-891f-0ce8a527c581 at (no spam) 24g2000hsh.googlegroups.com>,
miki <miki.livne at (no spam) gmail.com> wrote:
Quote: 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
In a sense, one can get a discrete white noise process;
one cannot get a continuous process of this type.
It is in continuous time that there is no such process.
The Wiener process does not quite satisfy a Lipshitz
condition of order 1/2, let alone enough to have a
derivative.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin at (no spam) stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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| illywhacker... |
| Posted: Wed May 21, 2008 9:46 am |
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Guest
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On May 5, 6:51 pm, miki <miki.li... at (no spam) gmail.com> wrote:
Quote: 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; |
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