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From: song cui on 23 Jul 2010 13:47
Hi ,

I want to design two bandpass filter:

1)They have same bandwidth but work at different center frequency. After same gaussian noise pass through those two filters, the output gaussian noise must be band-limited gaussian noise.Because those two filter have same bandwidth, the output noise should have same or very closed energy. But after I simulated, I found that the difference of energy is very big, when this difference compares to any of two output noise energy, the ratio is over 60%. I try to change noise length to do more tests, the results are all very bad.

2) To verify whether filters have change the properties of gaussian noise, I generate two samples of gaussian noise with same average power and length, I do not pass these two noise samples to any filter, so they are true gaussian noise. I compare energy of these two noise, the difference is very small, it is only 3%. when I increase the length of noise sample, the difference become smaller.
3) So I think that those two filter have changed some properties of gaussian noise. I read some books about this, maybe gaussian noise have been change d to color noise, not white noise again. I try two add whitening filter , it dosen't improve.


Can anybody help me at this problem? I have spent lots of time at it. If you can help me out of this problem, I will be very appreciated.

Thanks
From: Wayne King on 23 Jul 2010 14:25
"song cui" <cuisonggxu(a)hotmail.com> wrote in message <i2ckip$8il$1(a)fred.mathworks.com>...
> Hi ,
>
> I want to design two bandpass filter:
>
> 1)They have same bandwidth but work at different center frequency. After same gaussian noise pass through those two filters, the output gaussian noise must be band-limited gaussian noise.Because those two filter have same bandwidth, the output noise should have same or very closed energy. But after I simulated, I found that the difference of energy is very big, when this difference compares to any of two output noise energy, the ratio is over 60%. I try to change noise length to do more tests, the results are all very bad.
>
> 2) To verify whether filters have change the properties of gaussian noise, I generate two samples of gaussian noise with same average power and length, I do not pass these two noise samples to any filter, so they are true gaussian noise. I compare energy of these two noise, the difference is very small, it is only 3%. when I increase the length of noise sample, the difference become smaller.
> 3) So I think that those two filter have changed some properties of gaussian noise. I read some books about this, maybe gaussian noise have been change d to color noise, not white noise again. I try two add whitening filter , it dosen't improve.
>
>
> Can anybody help me at this problem? I have spent lots of time at it. If you can help me out of this problem, I will be very appreciated.
>
> Thanks

Hi Song Cui,
If you pass a white noise random process through a linear time-invariant operator (filter), the autocorrelation of the output is the convolution of the white noise autocorrelation with the deterministic autocorrelation of the filter. Accordingly the output autocorrelation will not be like that of a white noise process.

Wayne
From: song cui on 25 Jul 2010 23:47
"Wayne King" <wmkingty(a)gmail.com> wrote in message <i2cmqu$1tf$1(a)fred.mathworks.com>...
> "song cui" <cuisonggxu(a)hotmail.com> wrote in message <i2ckip$8il$1(a)fred.mathworks.com>...
> > Hi ,
> >
> > I want to design two bandpass filter:
> >
> > 1)They have same bandwidth but work at different center frequency. After same gaussian noise pass through those two filters, the output gaussian noise must be band-limited gaussian noise.Because those two filter have same bandwidth, the output noise should have same or very closed energy. But after I simulated, I found that the difference of energy is very big, when this difference compares to any of two output noise energy, the ratio is over 60%. I try to change noise length to do more tests, the results are all very bad.
> >
> > 2) To verify whether filters have change the properties of gaussian noise, I generate two samples of gaussian noise with same average power and length, I do not pass these two noise samples to any filter, so they are true gaussian noise. I compare energy of these two noise, the difference is very small, it is only 3%. when I increase the length of noise sample, the difference become smaller.
> > 3) So I think that those two filter have changed some properties of gaussian noise. I read some books about this, maybe gaussian noise have been change d to color noise, not white noise again. I try two add whitening filter , it dosen't improve.
> >
> >
> > Can anybody help me at this problem? I have spent lots of time at it. If you can help me out of this problem, I will be very appreciated.
> >
> > Thanks
>
> Hi Song Cui,
> If you pass a white noise random process through a linear time-invariant operator (filter), the autocorrelation of the output is the convolution of the white noise autocorrelation with the deterministic autocorrelation of the filter. Accordingly the output autocorrelation will not be like that of a white noise process.
>
> Wayne



> Hi Wayne

Thanks for your response. Can you find some methods to resolve this problem?
I hope that the energy difference of two output noise are very close. How about whitening filter? I am not too familiar to this kind of filter, I am trying it. Do you know any other good methods?
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