I missed a word in my statement, it should have read “signal properties”
instead
of signal. If you take the expectation value of any statistical moment,
the autocorrelation
function or any other significant characteristic you will get the the
expectation
value of the corresponding random process.
The most basic Walsh-Hadamard Transform does precisely as much mixing as
a DCT/DST/FFT of similar length.
Sure - and we'd expect WHT coeffs of iid noise to be Gaussian right? My
intent with the scare quotes on mixing there was a hand-wave to the
various relaxed conditions wherein the CLT still
On 01 Nov 2014, at 02:39, Ethan Duni ethan.d...@gmail.com wrote:
The expectation value of the signal over the ensemble of all unitary
transforms
with a suitable measure (like Haar).
The expected value you describe is equal to the zero signal (this follows
immediately from symmetry), not a
Hi music DSpers,
Maybe running the risk of starting a Griffin-Gate,
but one more consideration for the people interested in
keeping the basics of digital processing a bit pure, and
maybe to learn a thing or two for those working and/or
hobby-ing around in the field.
Just like there is some
There is a theorem that goes something like this:
If you have white noise expressed in one orthonormal basis, and you
transform it to another orthonormal basis, the result will still be white
noise.
The phrasing of that is obviously imprecise, but the point is this: since
the time and Fourier
Say we're only taking one length of the FFT transform, and
are only interested in the volume of the various output bins.
Now, how probable is it that we get all equal frequency amounts as
the output of the this FFT transform (without regarding phase), taking
for instance 256 or 4096 bins, and 16
I am not sure if the PDFs are preserved across
transforms from one orthonormal basis to
another, and the answer to your question would
depend on that (Of course it would also depend
on several other parts of the phrasing of your question
that aren't clear to me). My intuition is that PDFs
are
On 31 Oct 2014, at 19:50, Bjorn Roche bj...@xowave.com wrote:
There is a theorem that goes something like this:
If you have white noise expressed in one orthonormal basis, and you
transform it to another orthonormal basis, the result will still be white
noise.
There is certainly no such
There is a theorem that goes something like this:
If you have white noise expressed in one orthonormal basis, and you
transform it to another orthonormal basis, the result will still be white
noise.
There is certainly no such theorem. For any noise signal you can define
a basis that contains
On 31 Oct 2014, at 23:31, Ethan Duni ethan.d...@gmail.com wrote:
If you have Gaussian i.i.d. noise, you can apply any unitary transform you
want and you will still end up with Gaussian i.i.d. noise. I believe that
this is the result Bjorn is referring to. Note that this doesn't work with
it's funny how you guys seem to go off in all kinds of not so connected
directions. Just to make clear my question is a serious one, with more
normal undergrad material connected than I have ever seen mentioned
here, consider this: if I have a sampled noise signal of some kind,
regardless how
The correct statement would be
that an arbitrary unitary transform of a Gaussian white noise signal is
*expected* to give a gaussian white noise signal.
What does *expected* mean in that sentence? The distribution of a unitary
transform of an i.i.d. Gaussian vector is i.i.d. Gaussian.
My point
On 01 Nov 2014, at 00:06, Ethan Duni ethan.d...@gmail.com wrote:
The correct statement would be
that an arbitrary unitary transform of a Gaussian white noise signal is
*expected* to give a gaussian white noise signal.
What does *expected* mean in that sentence? The distribution of a
The expectation value of the signal over the ensemble of all unitary
transforms
with a suitable measure (like Haar).
The expected value you describe is equal to the zero signal (this follows
immediately from symmetry), not a Gaussian white noise signal (whatever
that is - you insist that it
On 2014-10-31, Theo Verelst wrote:
Now, how probable is it that we get all equal frequency amounts as
the output of the this FFT transform (without regarding phase), taking
for instance 256 or 4096 bins, and 16 bits accuracy ?! Or, how long
would we have to average the bin values to end up
On 2014-10-31, Bjorn Roche wrote:
I am not sure if the PDFs are preserved across transforms from one
orthonormal basis to another, and the answer to your question would
depend on that
They most certainly are not. As two concrete examples of bases which
lead to different induced PDFs upon
On 2014-10-31, Ethan Duni wrote:
Transforms between orthogonal bases are basically rotations. I.e.,
they are linear operators that produce each component of the output as
a linear combination of input components. Generally, then, the Central
Limit Theorem tells us that the output
On 2014-10-31, Theo Verelst wrote:
if I have a sampled noise signal of some kind, regardless how I got
it, it isn't going to make a difference for the main characteristics
of the proposed measurement which transformation I use, [...]
Oh, but it is. Suppose you derived your so called noise
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