Auto power spectrum

hi,

I have created a random binary noise using 2 methods. My main aim is to
create a random binary noise whose auto power spectrum rolls of at 1Hz(cut
off) and the attenuation should be sharp which is my spectrum pass band
should end near 2Hz.

first method:

I used a random gaussian noise by a sampling frequency 40Hz and compared
it with sinusoidal signal whose frequency is 0.3Hz with an amplitude of 2
so that if the reference is greater than the noise amplide then the
resultant will be 1 and otherwise zero. When I did the auto power spectrum
calculation for this it rolls of at 1Hz but the pass band ends near 3Hz
which is not what i need.

Second method:

I used a random gaussian noise with a sampling frequency of 120Hz. I then
filtered this one using a butter(5,0.0083,'low') an applied these
coefficients to the filter. After that if the signal is greater than 0
then resultant 1 otherwise 0. The auto power spectrum here also shows a
similar result as the previous one.

My question here is whether the methods i am appreaching to get a random
binary noise right and if not can anyone suggest me an another method.

My next question would be if this is right then is there a method in order
to make my attenuation sharper i.e., whether i can make the roll of to fall
from 1Hz to 2Hz.

I hope i am clear with my question. Any help on this would be great.

Thanks in advance 
Pavan

On Sep 15, 7:41 am, "pa1kumar" <pavan352...@yahoo.com> wrote:
> hi,
>
> I have created a random binary noise using 2 methods. My main aim is to
> create a random binary noise whose auto power spectrum rolls of at 1Hz(cut
> off) and the attenuation should be sharp which is my spectrum pass band
> should end near 2Hz.
>
> first method:
>
> I used a random gaussian noise by a sampling frequency 40Hz and compared
> it with sinusoidal signal whose frequency is 0.3Hz with an amplitude of 2
> so that if the reference is greater than the noise amplide then the
> resultant will be 1 and otherwise zero. When I did the auto power spectrum
> calculation for this it rolls of at 1Hz but the pass band ends near 3Hz
> which is not what i need.
>
> Second method:
>
> I used a random gaussian noise with a sampling frequency of 120Hz. I then
> filtered this one using a butter(5,0.0083,'low') an applied these
> coefficients to the filter. After that if the signal is greater than 0
> then resultant 1 otherwise 0. The auto power spectrum here also shows a
> similar result as the previous one.
>
> My question here is whether the methods i am appreaching to get a random
> binary noise right and if not can anyone suggest me an another method.
>
> My next question would be if this is right then is there a method in order
> to make my attenuation sharper i.e., whether i can make the roll of to fall
> from 1Hz to 2Hz.
>
> I hope i am clear with my question. Any help on this would be great.
>
> Thanks in advance
> Pavan

There won't be much coming out of your filter - it will look a bit
like a random walk - integrated white noise.
You can make the roll-off as sharp as you like with an FIR filter if
you can stand a time-delay? Define the dB attenuation you require at
2Hz and you can work out the order of say a Butterworth to do it. We
have

dB = 10Log10(1+V^(2n) )

where V=2 and dB = say 100 then solve for n and ^ represents' to the
power of'

It's gonna be big! The phase shift will be nasty too.

Hardy






Hardy

HardySpicer wrote:

> I   ...  The phase shift will be nasty too.

With random phase going in, how could you tell?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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