# 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?

Your opinion matters a lot.

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 Thanks as always for your reply. 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