On Mar 12, 5:16�am, Tim Wescott <t...@seemywebsite.now> wrote:
> HardySpicer wrote:
> > On Mar 10, 3:22 am, "msarovar" <mo...@grommit.com> wrote:
> >> Hi,
>
> >> What is the most efficient way to generate a noise process that is Gaussian
> >> correlated in time from a white noise process?
>
> >> I'm having trouble coming up with a simple FIR filter that will do this.
>
> >> Any suggestions?
>
> >> Thanks,
> >> ~mohan
>
> > Bit confused here. If you pass Guassian white noise through a LTI
> > filter the output is still Guassian but coloured.
>
> He wants noise that is colored in such a way that the autocorrelation is
> Gaussian.
>
> --
> Tim Wescott
> Control system and signal processing consultingwww.wescottdesign.com
Oh... weird..
Reply by Tim Wescott●March 11, 20102010-03-11
HardySpicer wrote:
> On Mar 10, 3:22 am, "msarovar" <mo...@grommit.com> wrote:
>> Hi,
>>
>> What is the most efficient way to generate a noise process that is Gaussian
>> correlated in time from a white noise process?
>>
>> I'm having trouble coming up with a simple FIR filter that will do this.
>>
>> Any suggestions?
>>
>> Thanks,
>> ~mohan
>
> Bit confused here. If you pass Guassian white noise through a LTI
> filter the output is still Guassian but coloured.
He wants noise that is colored in such a way that the autocorrelation is
Gaussian.
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Reply by HardySpicer●March 11, 20102010-03-11
On Mar 10, 3:22�am, "msarovar" <mo...@grommit.com> wrote:
> Hi,
>
> What is the most efficient way to generate a noise process that is Gaussian
> correlated in time from a white noise process?
>
> I'm having trouble coming up with a simple FIR filter that will do this.
>
> Any suggestions?
>
> Thanks,
> ~mohan
Bit confused here. If you pass Guassian white noise through a LTI
filter the output is still Guassian but coloured.
Hardy
Reply by Andor●March 10, 20102010-03-10
On 10 Mrz., 05:35, Jerry Avins <j...@ieee.org> wrote:
> Andor wrote:
> > On 9 Mrz., 15:22, "msarovar" <mo...@grommit.com> wrote:
> >> Hi,
>
> >> What is the most efficient way to generate a noise process that is Gaussian
> >> correlated in time from a white noise process?
>
> >> I'm having trouble coming up with a simple FIR filter that will do this.
>
> >> Any suggestions?
>
> >> Thanks,
> >> ~mohan
>
> > This link is three years old but still works:
>
> >http://math.mit.edu/~stevenj/preprints/iir-colored-noise-2007-03-13.pdf
>
> > It describes the use of IIR filters to efficiently (wrt to computer
> > time and memory) generate correlated sequences from white sequences.
>
> Any low-pass filter's output is correlated at high-enough frequencies.
Of course. The trick is to get the correlation you want as cheap as
possible.
Reply by Jerry Avins●March 10, 20102010-03-10
Andor wrote:
> On 9 Mrz., 15:22, "msarovar" <mo...@grommit.com> wrote:
>> Hi,
>>
>> What is the most efficient way to generate a noise process that is Gaussian
>> correlated in time from a white noise process?
>>
>> I'm having trouble coming up with a simple FIR filter that will do this.
>>
>> Any suggestions?
>>
>> Thanks,
>> ~mohan
>
> This link is three years old but still works:
>
> http://math.mit.edu/~stevenj/preprints/iir-colored-noise-2007-03-13.pdf
>
> It describes the use of IIR filters to efficiently (wrt to computer
> time and memory) generate correlated sequences from white sequences.
Any low-pass filter's output is correlated at high-enough frequencies.
Jerry
--
Physics is like sex: sure, it may give some practical results, but
that's not why we do it. -- Richard P. Feynman (Nobel Prize, Physics)
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Reply by msarovar●March 9, 20102010-03-09
>On 9 Mrz., 15:22, "msarovar" <mo...@grommit.com> wrote:
>> Hi,
>>
>> What is the most efficient way to generate a noise process that is
Gaussian
>> correlated in time from a white noise process?
>>
>> I'm having trouble coming up with a simple FIR filter that will do
this.
>>
>> Any suggestions?
>>
>> Thanks,
>> ~mohan
>
>This link is three years old but still works:
>
>http://math.mit.edu/~stevenj/preprints/iir-colored-noise-2007-03-13.pdf
>
>It describes the use of IIR filters to efficiently (wrt to computer
>time and memory) generate correlated sequences from white sequences.
>
>Regards,
>Andor
>
Great, thanks guys.
I will read more about Chebyshev filters. They sound like my solution.
Cheers,
~mohan
Reply by Andor●March 9, 20102010-03-09
On 9 Mrz., 15:22, "msarovar" <mo...@grommit.com> wrote:
> Hi,
>
> What is the most efficient way to generate a noise process that is Gaussian
> correlated in time from a white noise process?
>
> I'm having trouble coming up with a simple FIR filter that will do this.
>
> Any suggestions?
>
> Thanks,
> ~mohan
>> On Mar 9, 6:22=A0am, "msarovar" <mo...@grommit.com> wrote:
>>> Hi,
>>>
>>> What is the most efficient way to generate a noise process that is
> Gaussi=
>> an
>>> correlated in time from a white noise process?
>>>
>>> I'm having trouble coming up with a simple FIR filter that will do
> this.
>>> Any suggestions?
>>>
>>> Thanks,
>>> ~mohan
>> By "Gaussian correlated" do you mean anything other than correlated
>> and Gaussian distributed?
>>
>> What have you tried and why do you think it hasn't worked?
>>
>> "most efficient" is a context dependent term. Are you concerned with
>> implementing in a 8-bit micro-controller, a supercomputer, an FPGA or
>> a PC? Do you mean efficient in your time or the processor's time or
>> memory space?
>>
>> Dale B. Dalrymple
>>
>>
>
> Hi,
> Thanks for the quick answers. And sorry for the lack of detail in my last
> message.
>
> First, by "Gaussian correlated" I mean colored noise for which the temporal
> correlations are Gaussian.
>
> What I have tried so far is to form a Gaussian FIR filter and convolve the
> white noise with it to get output that is Gaussian correlated in time. I am
> running this on a PC but need to do it many, many times and so efficiency
> (in time, not memory) is important. Currently, the convolution is the
> limiting step in my code and I was wondering if there was an easier way to
> do this.
>
> For example, is there a recursive (IIR) filter for generating Gaussian
> correlations that might decrease the number of convolution steps?
>
"I'm having trouble coming up with a simple FIR filter that will do this"
Thus, no one suggests the obvious.
Yes, there are IIR filters that will approximate a Gaussian filter. In
continuous time these are referred to as "Bessel filters"; I don't know
how they've acquired a different name in the sampled time domain.
No matter what, you'll only get an approximation.
The FFT of a white Gaussian noise process is itself white Gaussian noise
with uniformly distributed phase. If you need finite-length vectors
with your Gaussian autocorrelation, you can make sequences with white
noise, shape them with the appropriate Gaussian envelope, then take the
inverse FFT to get a sequence with your desired time-domain properties.
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Reply by msarovar●March 9, 20102010-03-09
>On Mar 9, 6:22=A0am, "msarovar" <mo...@grommit.com> wrote:
>> Hi,
>>
>> What is the most efficient way to generate a noise process that is
Gaussi=
>an
>> correlated in time from a white noise process?
>>
>> I'm having trouble coming up with a simple FIR filter that will do
this.
>>
>> Any suggestions?
>>
>> Thanks,
>> ~mohan
>
>By "Gaussian correlated" do you mean anything other than correlated
>and Gaussian distributed?
>
>What have you tried and why do you think it hasn't worked?
>
>"most efficient" is a context dependent term. Are you concerned with
>implementing in a 8-bit micro-controller, a supercomputer, an FPGA or
>a PC? Do you mean efficient in your time or the processor's time or
>memory space?
>
>Dale B. Dalrymple
>
>
Hi,
Thanks for the quick answers. And sorry for the lack of detail in my last
message.
First, by "Gaussian correlated" I mean colored noise for which the temporal
correlations are Gaussian.
What I have tried so far is to form a Gaussian FIR filter and convolve the
white noise with it to get output that is Gaussian correlated in time. I am
running this on a PC but need to do it many, many times and so efficiency
(in time, not memory) is important. Currently, the convolution is the
limiting step in my code and I was wondering if there was an easier way to
do this.
For example, is there a recursive (IIR) filter for generating Gaussian
correlations that might decrease the number of convolution steps?
Thanks again for the help,
~mohan
Reply by dbd●March 9, 20102010-03-09
On Mar 9, 6:22�am, "msarovar" <mo...@grommit.com> wrote:
> Hi,
>
> What is the most efficient way to generate a noise process that is Gaussian
> correlated in time from a white noise process?
>
> I'm having trouble coming up with a simple FIR filter that will do this.
>
> Any suggestions?
>
> Thanks,
> ~mohan
By "Gaussian correlated" do you mean anything other than correlated
and Gaussian distributed?
What have you tried and why do you think it hasn't worked?
"most efficient" is a context dependent term. Are you concerned with
implementing in a 8-bit micro-controller, a supercomputer, an FPGA or
a PC? Do you mean efficient in your time or the processor's time or
memory space?
Dale B. Dalrymple