Noise modeling ideas

On Jun 9, 7:54&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On Jun 9, 1:50&#4294967295;pm, brent <buleg...@columbus.rr.com> wrote:
>
>
>
>
>
>
>
>
>
> > I am working on a program to display a noise signal. &#4294967295;It contains 100
> > random amplitude sine waves and 100 random amplitude cosine waves from
> > 1-100 Hz. &#4294967295;I am trying to refresh the screen with the wave form as
> > fast as I can. &#4294967295;each waveform is 400 points long. &#4294967295;This is
> > computationally a real processor hog. &#4294967295;I have stored all 100 sine
> > waves and 100 cosine waves in an array so I am just applying the
> > random number creation to each wave and summing them up. &#4294967295;I am doing
> > this brute force, but i have somewhat optimized what I have done thus
> > far. (BTW my random amplitude is done by summing three random number
> > generations together to try to achieve a more Gaussian distribution on
> > the amplitudes)
>
> > I am using 40% of my computer processor to refresh this 1 time per
> > second. ( I deliberately use a somewhat crummy computer when doing
> > this)
>
> > Any ideas for creating a computationally efficient noise in the time
> > domain that contains 100 frequencies and actually looks like noise
> > when its done?
>
> If you want a *noise* signal, use a random number generator.
>
> If you want a sum-of-sines signal, use a look-up table.
>
> Rune

I am currently doing a sum of sines and I am using a lookup table to
store all the sine values of the 200 sine/cosine waves from 1-100 Hz.
I want to use sum of sines so that the end user (this will be a noise
tutorial) can take out frequencies (use filtering) and see the effect
on the noise signal.  I apply a random process to apply an aplitude to
each sine/cosine.  I see a lot of good information in this thread
about how to properly build noise with random processes, but i think i
need the sum of sines/cosines approach.  Oh well, I will probably have
to limit the update rate to once per second.

Thanks all.

You could use an inverse FFT to generate a time waveform with defined frequency content. Apply your random numbers to the complex bin values.

john

On Jun 11, 7:13&#4294967295;am, John <sampson...@gmail.com> wrote:
> You could use an inverse FFT to generate a time waveform with defined frequency content. Apply your random numbers to the complex bin values.
>
> john


I have thought about that a little bit.  I would need a 512 point
FFT.  I have written a 64 point FFT that comfortably runs 10-15 times
per second.  I have not looked up how much extra processing a 512
point would take, but I am afraid that a 512 is more than 10 times
longer than a 64 point FFT.

thanks for the idea

brent

On 11-06-2011 @ 12:54:28 brent <bulegoge@columbus.rr.com> wrote:

(...)
> I want to use sum of sines so that the end user (this will be a noise
> tutorial) can take out frequencies (use filtering) and see the effect
> on the noise signal.
(...)


So you don't need  sum of sines
to filter out a little bit of perfect noise.
Or you measure the energy of noise....
I'm interested about effects of filtering noise
and what it has common to do with a method of generating it.


-- 
Mikolaj

>On Jun 9, 2:45=A0pm, "taks" <mtakatz@n_o_s_p_a_m.verasent.com> wrote:
>> >Z1 =3D sqrt(-2 * log(R1)) * cos(2 * pi * R2); % MATLAB syntax
>> >Z2 =3D sqrt(-2 * log(R2)) * sin(2 * pi * R2);
>>
>> I should add that though these equations can be found on the web in
vario=
>us
>> places, I actually got them out of "Discrete-Event System Simulation"
by
>> Jerry Banks, et al. =A0Not a bad text I might add.
>>
>> Mark
>
>Is there a typo in these equations (as published in comp.dsp)
>or are they an exact copy of what is in the text cited, in which
>case the typo is in the textbook, and is being reproduced here?

Typo - my bad.  The 2nd equation should be log(R1).

Mark

>1. Your formulae are wrong.

Only the typo is incorrect.  If this is being generated on a floating point
machine, the use of doubles will resolve the tails issue.

Mark

>>1. Your formulae are wrong.
>
>Only the typo is incorrect.  If this is being generated on a floating
point
>machine, the use of doubles will resolve the tails issue.
>
>Mark
>

One problem you need to be aware of is the possibility of actually getting
a 0 in R1.  The frequency of such an occurrence is obviously reduced with
higher precision in R1 (the "tails" issue.)  I saw an iterative approach
online once but I don't recall if it was simply checking for a 0 (IIRC, it
was a bit more than that.)

I have not tried VV's approach before - this was in a class I taught out of
the text I referenced (Banks did not refer to it as the B-M method, oddly,
though I have seen that online as well.)

Mark

On Jun 11, 12:54&#4294967295;pm, brent <buleg...@columbus.rr.com> wrote:
> On Jun 9, 7:54&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
>
>
>
>
>
> > On Jun 9, 1:50&#4294967295;pm, brent <buleg...@columbus.rr.com> wrote:
>
> > > I am working on a program to display a noise signal. &#4294967295;It contains 100
> > > random amplitude sine waves and 100 random amplitude cosine waves from
> > > 1-100 Hz. &#4294967295;I am trying to refresh the screen with the wave form as
> > > fast as I can. &#4294967295;each waveform is 400 points long. &#4294967295;This is
> > > computationally a real processor hog. &#4294967295;I have stored all 100 sine
> > > waves and 100 cosine waves in an array so I am just applying the
> > > random number creation to each wave and summing them up. &#4294967295;I am doing
> > > this brute force, but i have somewhat optimized what I have done thus
> > > far. (BTW my random amplitude is done by summing three random number
> > > generations together to try to achieve a more Gaussian distribution on
> > > the amplitudes)
>
> > > I am using 40% of my computer processor to refresh this 1 time per
> > > second. ( I deliberately use a somewhat crummy computer when doing
> > > this)
>
> > > Any ideas for creating a computationally efficient noise in the time
> > > domain that contains 100 frequencies and actually looks like noise
> > > when its done?
>
> > If you want a *noise* signal, use a random number generator.
>
> > If you want a sum-of-sines signal, use a look-up table.
>
> > Rune
>
> I am currently doing a sum of sines and I am using a lookup table to
> store all the sine values of the 200 sine/cosine waves from 1-100 Hz.
> I want to use sum of sines so that the end user (this will be a noise
> tutorial) can take out frequencies (use filtering) and see the effect
> on the noise signal. &#4294967295;I apply a random process to apply an aplitude to
> each sine/cosine. &#4294967295;I see a lot of good information in this thread
> about how to properly build noise with random processes, but i think i
> need the sum of sines/cosines approach. &#4294967295;Oh well, I will probably have
> to limit the update rate to once per second.

If this is a demo, I'd rather relax on the on-line requirement.
Instead of an online app, I'd model the data in memory once
(maybe 30-60 seconds worth of data) and then display those data
in a loop.

If / when the user plays with the bandwidth, model again and
start a new loop.

Rune