# maximum accuracy of estimating the power of the signal

Started by September 13, 2003
```Hello,

To what accuracy can i estimate the power of a signal.what are the
different techniques to increase the accuracy of estimating the power
of the signal.I am required to estimate the power of the signal to the
accuracy of 10^-7 (i.e. the difference between estimated and actual
power). I am giving the matlab code for estimating the power of the
signal. In my stimation the accuracy i am getting is only 10^-5 to
10^-6 i am required to increase the estimated to an accuracy of 10^-7.
What all techniques can i use.... my noise amplitude amp is fixed at
.008.

praveen

%clear;am=1;f1=20;f2=50;fs=500;N=5000;kk=512;bw=5;amp=.008;frq1=20;amp_estimate;er

%  signal generation
s=am*cos(2*pi*f1/fs*[1:N])+cos(2*pi*f2/fs*[1:N])+amp*randn(1,N);
% To filter other signal other than f1 frequency whose amplitude to be
estimated
[a1,b1]=ellip(3,.0001,60,[f1-2 f1+2]/fs*2);
s=filter(a1,b1,s);
% Noncoherent integration
i=cos(2*pi*frq1/(fs)*[0:(length(s)-1)]);Si=s.*i;
q=sin(2*pi*frq1/(fs)*[0:(length(s)-1)]);Sq=s.*q;
[a,b]=fir1(kk,bw/(fs)*2);
Si=filter(a,b,Si);
Sq=filter(a,b,Sq);
% finding the power
A=sqrt(Si.^2+Sq.^2);
S1=mean(A(kk:end));
%difference between the estimated and actual power of signal
er=S1-(am^2)/2;
```
```praveenkumar1979@rediffmail.com (praveen) wrote in message news:<ff8a3afb.0309122155.12ecc64d@posting.google.com>...
> Hello,
>
> To what accuracy can i estimate the power of a signal.what are the
> different techniques to increase the accuracy of estimating the power
> of the signal.I am required to estimate the power of the signal to the
> accuracy of 10^-7 (i.e. the difference between estimated and actual
> power). I am giving the matlab code for estimating the power of the
> signal. In my stimation the accuracy i am getting is only 10^-5 to
> 10^-6 i am required to increase the estimated to an accuracy of 10^-7.
> What all techniques can i use.... my noise amplitude amp is fixed at
> .008.

- You need to look at the variance of your estimator for power. As you know,
estimating some parameter in a (partially) random signal requires statistical
methods. The performance of any estimator can be described in terms of mean
and variance. You should be able to investigate the variance of your
particular estimator, and see how the variance varies with e.g. the number
of data points going into your estimate.

- Once you have done that, you may want to check out the Cramer-Rao lower
Bound (CRB) on estimator variance. The CRB expresses the lowest possible
limit on your variance, given Signal-to-Noise Ration (SNR), the number of
sata points available and the mathematical expression for your estimator.
It is important to realize that your required precision of the estimate
*may* be too tough, i.e. that the CRB may not let you reach it with the
amount of data you have available.

The connection between the estimator variance and the CRB is that each
estimator is characterized by a variance (given SNR and amounts of data),
while the CRB expresses the lowest possible variance. The variance of
any estimator may or may not approach the CRB. The only way to actually
reach the CRB is to design an estimator for that particular purpose. This
may or may not be possible.

Rune
```
```praveen wrote:
>
> Hello,
>
> To what accuracy can i estimate the power of a signal.what are the
> different techniques to increase the accuracy of estimating the power
> of the signal.I am required to estimate the power of the signal to the
> accuracy of 10^-7 (i.e. the difference between estimated and actual
> power). I am giving the matlab code for estimating the power of the
> signal. In my stimation the accuracy i am getting is only 10^-5 to
> 10^-6 i am required to increase the estimated to an accuracy of 10^-7.
> What all techniques can i use.... my noise amplitude amp is fixed at
> .008.
>
> praveen
>
> %clear;am=1;f1=20;f2=50;fs=500;N=5000;kk=512;bw=5;amp=.008;frq1=20;amp_estimate;er
>
> %  signal generation
> s=am*cos(2*pi*f1/fs*[1:N])+cos(2*pi*f2/fs*[1:N])+amp*randn(1,N);
> % To filter other signal other than f1 frequency whose amplitude to be
> estimated
> [a1,b1]=ellip(3,.0001,60,[f1-2 f1+2]/fs*2);
> s=filter(a1,b1,s);
> % Noncoherent integration
> i=cos(2*pi*frq1/(fs)*[0:(length(s)-1)]);Si=s.*i;
> q=sin(2*pi*frq1/(fs)*[0:(length(s)-1)]);Sq=s.*q;
> [a,b]=fir1(kk,bw/(fs)*2);
> Si=filter(a,b,Si);
> Sq=filter(a,b,Sq);
> % finding the power
> A=sqrt(Si.^2+Sq.^2);
> S1=mean(A(kk:end));
> %difference between the estimated and actual power of signal
> er=S1-(am^2)/2;

It helps to calculate power and not "voltage": try

A=Si.^2+Sq.^2;

A=sqrt(Si.^2+Sq.^2);

. (Doh!)
--
%% Fuquay-Varina, NC            %       'cause no one knows which side
%%% 919-577-9882                %                   the coin will fall."
%%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
```
```Hello Mr Rune,
Given the flexiblity in choosing the number of data point can i get
the accuracy of 10^-7. Can you please explain me the cramer rao lower
bound (equation that relates SNR, Number of data and the mathematical
expression of the estimator)

praveen
```
```On 12 Sep 2003 22:55:36 -0700, praveenkumar1979@rediffmail.com
(praveen) wrote:

>Hello,
>
>To what accuracy can i estimate the power of a signal.what are the
>different techniques to increase the accuracy of estimating the power
>of the signal.I am required to estimate the power of the signal to the
>accuracy of 10^-7 (i.e. the difference between estimated and actual
>power). I am giving the matlab code for estimating the power of the
>signal. In my stimation the accuracy i am getting is only 10^-5 to
>10^-6 i am required to increase the estimated to an accuracy of 10^-7.
>What all techniques can i use.... my noise amplitude amp is fixed at
>.008.
>
>praveen

Hi,
just out of curiosity, what is the
application where you need such
high accuracy?

Maybe it's an audio application.
You audioheads like high performance, right?

[-Rick-]

```
```praveenkumar1979@rediffmail.com (praveen) wrote in message news:<ff8a3afb.0309150038.552a2587@posting.google.com>...
> Hello Mr Rune,
> Given the flexiblity in choosing the number of data point can i get
> the accuracy of 10^-7. Can you please explain me the cramer rao lower
> bound (equation that relates SNR, Number of data and the mathematical
> expression of the estimator)

You find the CRB in texts on statistics and Statistical Signal Processing.
Try any of these:

Kay:          Modern Spectral Estimation - Theory & Applications
Prentice-Hall 1988

Therrien:     Discrete Random Signals and Statistical Signal Processing
Prentice-Hall, 1992

Stuart & Ord: Kendall's advanced theory of statistics, vol 2A
Oxford University Press, 1998

van Trees:    Optimum Array Processing
Wiley, 2002

Rune
```
```Hello Mr Rick Lyon,
The application is for a DSP based Fiber optic gyroscope when the
accuracy of the phase measurement is to be done at this accuracy.

With regards
praveen
```
```praveen,
Now you have ME interested.  Are you using the microbending property
to form a fiber-optic sensor?  If you need that kind of accuracy for
the phase measurement, it would imply to me that you are using a
interferometric-based sensor.  If so, why this and not one of the
other sensor types (fiber-optic of course)?  If not, can you talk
about what you're basing the sensor on?

Murice Givens

praveenkumar1979@rediffmail.com (praveen) wrote in message news:<ff8a3afb.0309152110.fd879c6@posting.google.com>...
> Hello Mr Rick Lyon,
> The application is for a DSP based Fiber optic gyroscope when the
> accuracy of the phase measurement is to be done at this accuracy.
>
> With regards
> praveen
```