# Normalizing Histogram

Started by June 25, 2009
Dear All

I am trying to plot histogram of the o/p of equalizer. As the o/p is
complex I will have to plot histogram of real and imaginary part
separately. I know it is straight forward in matlab, but the problem is how
to normalize y-axis.

The modulation I am using is 4-QAM. As this will be bimodal distribution
around +1 and -1, I am thinking to do following:

1. find std deviation (\sigma) of real(x_hat)>0 (which should be equal to
std deviation of real(x_hat)<0).

2. Nromalize the histogram between 0 and 1 and then scale it again with
1/(sigma*sqrt(2*pi)).

Is this correct? or any other way to do it?

Thanks

Best Regards,

Chintan

On Jun 25, 10:42&#2013266080;am, "cpshah99" <cpsha...@rediffmail.com> wrote:
> Dear All
>
> I am trying to plot histogram of the o/p of equalizer. As the o/p is
> complex I will have to plot histogram of real and imaginary part
> separately. I know it is straight forward in matlab, but the problem is how
> to normalize y-axis.
>
> The modulation I am using is 4-QAM. As this will be bimodal distribution
> around +1 and -1, I am thinking to do following:
>
> 1. find std deviation (\sigma) of real(x_hat)>0 (which should be equal to
> std deviation of real(x_hat)<0).
>
> 2. Nromalize the histogram between 0 and 1 and then scale it again with &#2013266080;
> 1/(sigma*sqrt(2*pi)).
>
> Is this correct? or any other way to do it?
>
> Your opinion matters a lot.
>
> Thanks
>
> Best Regards,
>
> Chintan

I'd say you should scale the height such that the sum of the bins
come out to 1.  Basically you scale it such that it becomes a
probability density estimate.

>I'd say you should scale the height such that the sum of the bins
>come out to 1.  Basically you scale it such that it becomes a
>probability density estimate.
>

Hi Julius

So, if there are 100 bins, then sum of these 100 bins should be equal to
1.?

Will this give me the y-axis to be p(\hat{x}/x) where \hat{x} is o/p of
equalizer and x is transmitted symbols?

Thanks again.

Chintan


>I'd say you should scale the height such that the sum of the bins
>come out to 1.  Basically you scale it such that it becomes a
>probability density estimate.
>

Hi All

Sorry to ask this damn thing again but I just need some confirmation.

I am not convinved with the solution that to normalize the histogram
(y-axis in terms of pdf) the sum of all bins has to be 1.

example: for Normal Distribution,

N=1e6;
x=randn(1,N);
[N1 X1]=hist(x,100); % 100 bins
subplot(211)
plot(X1,N1/sum(N1))

will have different solution when number of bins increase

[N2 X2]=hist(x,200);
subplot(212)
plot(X2,N2/sum(N2))

but I think it should be

figure
[N3 X3]=hist(x,100);
subplot(211)
plot(X3,1/(sqrt(2*pi)*std(x))*N3/max(N3))

[N4 X4]=hist(x,200);
subplot(212)
plot(X4,1/(sqrt(2*pi)*std(x))*N4/max(N4))

I might be wrong but it will be really great if anybody can throw light on
this.

Chintan