Noise processing

Hi all,

I am working on a project where I am trying to detect the direct path
signal for ranging purposes using UWB technology. I am developing an
algorithm that accounts for noise, but am still not sure how to account for
the noise. I know I can't use the noise mean because that should be zero. I
am pretty sure I should be using the variance but do not exactly understand
why. Can anyone explain to me the significance of the noise variance as
opposed to the noise mean in a signal? Or can anyone direct me to
literature that discusses the processing of noise? Thanks.

-jyproc

On Jun 24, 9:15&#4294967295;pm, "jyproc" <jyaqu...@gmail.com> wrote:
> Hi all,
>
> I am working on a project where I am trying to detect the direct path
> signal for ranging purposes using UWB technology. I am developing an
> algorithm that accounts for noise, but am still not sure how to account for
> the noise. I know I can't use the noise mean because that should be zero. I
> am pretty sure I should be using the variance but do not exactly understand
> why. Can anyone explain to me the significance of the noise variance as
> opposed to the noise mean in a signal? Or can anyone direct me to
> literature that discusses the processing of noise? Thanks.
>
> -jyproc

I'm not sure what exactly you are looking for.
But let's try a simple example.  Suppose there is
a value A that you are looking to estimate based
on a set of observations:

  y_n = A + w_n,  n = 0,1,...,N-1.

Let's now say that w_n are Gaussian noise terms
with variance \sigma^2 and mean 0.

OK, so intuitively (and formally) the best estimate
is given by:

  \hat{A} = 1/N \sum_n y_n.

Then one way to assess the quality of your estimate
is to look at the mean-square error:

  E[  | \hat{A} - A |^2 ]

Now do some algebra and probability and you see
how \sigma^2 effects this.

Does that help?

Julius

Noise variance is the measure of noise power.

the power of a noise signal is given by the 
following expression

noise_power = (mean*mean) + variance   ...... Eq 1

for noisy signals whose mean is zero, the variance
indicates the power of the noisy signal.

the above equation is true for periodic signals 
too like sine, square, triangular, etc.

signal to noise ratio is a very important term
to evaluate the performance of the datapath module.

SNR = 10*log10(sig_pow/noi_pow)

for periodic signals we know how to compute signal
power. so only thing left is how to compute noise
power, which is as mentioned in equation 1.

If you look at the "physics" definition of RMS, things
will be much more clearrer, RMS is defined as an equivalent
amount of power dissipated by the dc source. then the dc
value of the source is same as the rms value of the varying
source.

Thanks and Best Regards

Bharat Pathak

Arithos Designs
www.Arithos.com

DSP Design Consultancy and Training Company.

Join us on Orkut community :
http://www.orkut.co.in/Community.aspx?cmm=52708286

>On Jun 24, 9:15=A0pm, "jyproc" <jyaqu...@gmail.com> wrote:
>> Hi all,
>>
>> I am working on a project where I am trying to detect the direct path
>> signal for ranging purposes using UWB technology. I am developing an
>> algorithm that accounts for noise, but am still not sure how to account
f=
>or
>> the noise. I know I can't use the noise mean because that should be
zero.=
> I
>> am pretty sure I should be using the variance but do not exactly
understa=
>nd
>> why. Can anyone explain to me the significance of the noise variance
as
>> opposed to the noise mean in a signal? Or can anyone direct me to
>> literature that discusses the processing of noise? Thanks.
>>
>> -jyproc
>
>I'm not sure what exactly you are looking for.
>But let's try a simple example.  Suppose there is
>a value A that you are looking to estimate based
>on a set of observations:
>
>  y_n =3D A + w_n,  n =3D 0,1,...,N-1.
>
>Let's now say that w_n are Gaussian noise terms
>with variance \sigma^2 and mean 0.
>
>OK, so intuitively (and formally) the best estimate
>is given by:
>
>  \hat{A} =3D 1/N \sum_n y_n.
>
>Then one way to assess the quality of your estimate
>is to look at the mean-square error:
>
>  E[  | \hat{A} - A |^2 ]
>
>Now do some algebra and probability and you see
>how \sigma^2 effects this.
>
>Does that help?
>
>Julius
>


Julius,

I have a waveform obtained from the receiver that displays the amplitude
received. I want to detect the first instance that corresponds to an actual
received signal and not noise. Sorry for not being clearer earlier. That's
why the algorithm should process the noise and account for it...to reduce
the likelihood of detecting a noise signal as a received signal. Thanks for
the help.

>Noise variance is the measure of noise power.
>
>the power of a noise signal is given by the 
>following expression
>
>noise_power = (mean*mean) + variance   ...... Eq 1
>
>for noisy signals whose mean is zero, the variance
>indicates the power of the noisy signal.
>
>the above equation is true for periodic signals 
>too like sine, square, triangular, etc.
>
>signal to noise ratio is a very important term
>to evaluate the performance of the datapath module.
>
>SNR = 10*log10(sig_pow/noi_pow)
>
>for periodic signals we know how to compute signal
>power. so only thing left is how to compute noise
>power, which is as mentioned in equation 1.
>
>If you look at the "physics" definition of RMS, things
>will be much more clearrer, RMS is defined as an equivalent
>amount of power dissipated by the dc source. then the dc
>value of the source is same as the rms value of the varying
>source.
>
>Thanks and Best Regards
>
>Bharat Pathak
>
>Arithos Designs
>www.Arithos.com
>
>DSP Design Consultancy and Training Company.
>
>Join us on Orkut community :
>http://www.orkut.co.in/Community.aspx?cmm=52708286
>
>
>

Thanks for the help.
So if all I need is the mean amplitude of the noise, I could simply use

average_noise_amplitude=the mean of the absolute value of all noise
samples. Right?

Thanks.
-jyproc

On 25 Jun, 15:36, "jyproc" <jyaqu...@gmail.com> wrote:

> So if all I need is the mean amplitude of the noise, I could simply use
>
> average_noise_amplitude=the mean of the absolute value of all noise
> samples. Right?

If you really want to look at the *amplitude* then yes.
But I doubt the result will be very helpful to you, since
most noise processes encountered in communications are
characterized as 'zero mean', referring to the mean of
the amplitude.

So you could have a lot of noise in your signal and still
have the mean amplitude equal 0.

The noise variance (which equals noise power in zero mean
processes) is a far more helpful number, since it can be
used in discussions about SNR and so on.

Rune

On Jun 25, 8:30 am, "jyproc" <jyaqu...@gmail.com> wrote:
> >On Jun 24, 9:15=A0pm, "jyproc" <jyaqu...@gmail.com> wrote:
> >> Hi all,
>
> >> I am working on a project where I am trying to detect the direct path
> >> signal for ranging purposes using UWB technology. I am developing an
> >> algorithm that accounts for noise, but am still not sure how to account
> f=
> >or
> >> the noise. I know I can't use the noise mean because that should be
> zero.=
> > I
> >> am pretty sure I should be using the variance but do not exactly
> understa=
> >nd
> >> why. Can anyone explain to me the significance of the noise variance
> as
> >> opposed to the noise mean in a signal? Or can anyone direct me to
> >> literature that discusses the processing of noise? Thanks.
>
> >> -jyproc
>
> >I'm not sure what exactly you are looking for.
> >But let's try a simple example.  Suppose there is
> >a value A that you are looking to estimate based
> >on a set of observations:
>
> >  y_n =3D A + w_n,  n =3D 0,1,...,N-1.
>
> >Let's now say that w_n are Gaussian noise terms
> >with variance \sigma^2 and mean 0.
>
> >OK, so intuitively (and formally) the best estimate
> >is given by:
>
> >  \hat{A} =3D 1/N \sum_n y_n.
>
> >Then one way to assess the quality of your estimate
> >is to look at the mean-square error:
>
> >  E[  | \hat{A} - A |^2 ]
>
> >Now do some algebra and probability and you see
> >how \sigma^2 effects this.
>
> >Does that help?
>
> >Julius
>
> Julius,
>
> I have a waveform obtained from the receiver that displays the amplitude
> received. I want to detect the first instance that corresponds to an actual
> received signal and not noise. Sorry for not being clearer earlier. That's
> why the algorithm should process the noise and account for it...to reduce
> the likelihood of detecting a noise signal as a received signal. Thanks for
> the help.

Well, start by describing your noise.  Is it white?  Gaussian?  Zero-
mean?
This determines what estimator/detector works.

>On Jun 25, 8:30 am, "jyproc" <jyaqu...@gmail.com> wrote:
>> >On Jun 24, 9:15=A0pm, "jyproc" <jyaqu...@gmail.com> wrote:
>> >> Hi all,
>>
>> >> I am working on a project where I am trying to detect the direct
path
>> >> signal for ranging purposes using UWB technology. I am developing
an
>> >> algorithm that accounts for noise, but am still not sure how to
account
>> f=
>> >or
>> >> the noise. I know I can't use the noise mean because that should be
>> zero.=
>> > I
>> >> am pretty sure I should be using the variance but do not exactly
>> understa=
>> >nd
>> >> why. Can anyone explain to me the significance of the noise
variance
>> as
>> >> opposed to the noise mean in a signal? Or can anyone direct me to
>> >> literature that discusses the processing of noise? Thanks.
>>
>> >> -jyproc
>>
>> >I'm not sure what exactly you are looking for.
>> >But let's try a simple example.  Suppose there is
>> >a value A that you are looking to estimate based
>> >on a set of observations:
>>
>> >  y_n =3D A + w_n,  n =3D 0,1,...,N-1.
>>
>> >Let's now say that w_n are Gaussian noise terms
>> >with variance \sigma^2 and mean 0.
>>
>> >OK, so intuitively (and formally) the best estimate
>> >is given by:
>>
>> >  \hat{A} =3D 1/N \sum_n y_n.
>>
>> >Then one way to assess the quality of your estimate
>> >is to look at the mean-square error:
>>
>> >  E[  | \hat{A} - A |^2 ]
>>
>> >Now do some algebra and probability and you see
>> >how \sigma^2 effects this.
>>
>> >Does that help?
>>
>> >Julius
>>
>> Julius,
>>
>> I have a waveform obtained from the receiver that displays the
amplitude
>> received. I want to detect the first instance that corresponds to an
actual
>> received signal and not noise. Sorry for not being clearer earlier.
That's
>> why the algorithm should process the noise and account for it...to
reduce
>> the likelihood of detecting a noise signal as a received signal. Thanks
for
>> the help.
>
>Well, start by describing your noise.  Is it white?  Gaussian?  Zero-
>mean?
>This determines what estimator/detector works.
>

I believe the noise is Additive White Gaussian Noise.

-jyproc

On Jun 25, 1:03 pm, "jyproc" <jyaqu...@gmail.com> wrote:

> I believe the noise is Additive White Gaussian Noise.
>
> -jyproc

OK, when the signal s(t) is known and you want to detect
it in the presence of AWGN, the optimal detector is
a correlator (of the received signal versus s(-t)), followed
by magnitude estimator and a threshold.

To set the threshold properly depends on s(t) and
the noise variance, since AWGN will appear at the output
of the correlator also.

Is this what you are looking for?

>
>Thanks for the help.
>So if all I need is the mean amplitude of the noise, I could simply use
>
>average_noise_amplitude=the mean of the absolute value of all noise
>samples. Right?


No, Not right.
mean_of_noise = mean(noise_samples); 

Regards
Bharat Pathak

Arithos Designs
www.Arithos.com

A Premier DSP Design Consultancy and Training Company.