Confusion about quantization noise calculation

[Julian18]

Hello there:
I am constructing a naive quantizer using matlab, with LSB=1. The output waveform seems good. but when I calculate the total quantization noise power, I fail to get a number that is around 1/12= 0.0833, on the contrary i always get 1/6=1.672. I know I must have done something very silly, so plz help me out there.
the matlab code is listed below as

clear x y ref;
N=8192*4;
ref=[-3.5:2.5];
x=rand(1,N)*8-4.5;
for i=1:N

y(i)=sum(x(i)>ref);​

QN(i)=y(i)-4-x(i);​

end
%QN=y-4-x;
s=abs(fft(QN));
s=s(1:end/2)/N*2;
sum(s.^2)

below shown are the quantization waveform and its spectrum

Thanks

 

[erikl]

... I fail to get a number that is around 1/12= 0.0833, on the contrary i always get 1/6=1.672. I know I must have done something very silly

Just a guess: s=s(1:end/2)/N*2; Does it divide or multiply by 2 ?
Of course this makes a quotient of 4 in the result, but perhaps the above given numbers represent the sqrt?

 

[Julian18]

Just a guess: s=s(1:end/2)/N*2; Does it divide or multiply by 2 ?
Of course this makes a quotient of 4 in the result, but perhaps the above given numbers represent the sqrt?

Hi erikl
I think it is multiplied by 2; cause what I really want is to divide s by N/2 which leads s to be divided by N and multiplied by 2;

 

[erikl]

I think it is multiplied by 2; cause what I really want is to divide s by N/2 which leads s to be divided by N and multiplied by 2;

Yes, I think this is correct: Division and multiplication usually own the same priority, and operations of the same priority are performed from left to right. You could make sure, however, by using brackets.