Problems with normalization in fourier transform

I worked with fft() in matlab and tried to get spectrum two variete ways: 1) fft() from signal itsefl 2) fft() from autocorrelation of signal

it worked out well, but I have problems with normalization. This is my code in Matlab:

clc;clear;close all;
%%generate a model signal in physical space
step_t=0.001; 
first_step=0;
last_step=1;
t=first_step:step_t:last_step;         

%%generate signal
Noise=0;
Noise=(wgn(1001,1,23))';
y=  50*sin(2*pi*30*t) + 20*cos(2*pi*60*t)+Noise;

%%plotting graph
figure('name', 'Signal and its Spectrum')
subplot(2,1,1), plot(t,y); title('Signal  10*sin(2*pi*60*t) 1000 points')

%%MatLab Guide
% http://www.mathworks.com/help/matlab/ref/fft.html , ñì. òàêæå ñòð 63 Ñåðãèåíêî
fourier=fft(y );     
N_=length(fourier);
f_ = (1 / step_t)  *   (   0:    (N_/2)   )    /    N_; 

a=(fourier.*conj(fourier))/(N_*N_); % Spectrum density. Which density have every frequency 
a = a(1:N_ /2+1);   % get half due to parity                                       
% a(2:end-1) = 4*a(2:end-1);  % NORMALIZATION!!
subplot(2,1,2), plot(f_ ,a ); title('Spectrum from signal')

%%through autocorrelation function 
% we have 1000 points, so ACF should be around 100 points
% but still there are problems with normalization  !    : - (
Avarage_value_of_signal = mean(y);
V=0;
S=0;
N_ = length(   y    );
ACF_signal=zeros(1,100);
for j=1:99;
    S=0;
    A=0;
    for i=1:N_ - j
        A= (  y(i) - Avarage_value_of_signal   )*(   y(i+j)    -     Avarage_value_of_signal     );
        S=S+A;
    end
    ACF_signal(j) = S    /   (i);
end

figure('name', 'ACF and its Spectrum'); subplot(2,1,1)
plot(ACF_signal);
title('  ACF and Spectrum  ');  grid on;

%%Spectrun from ACF
% and again no clue about normalization! 
fourier=fft(ACF_signal );     
N_=length(fourier);
f_ = (1 / step_t)  *   (   0:    (N_/2)   )    /    N_; 

a=(fourier.*conj(fourier))/(N_*N_);  
a = a(1:N_ /2+1);                                     
%a(2:end-1) = 4*a(2:end-1); 
subplot(2,1,2), plot(f_ ,a ); title('Spectrum from ACF');

As you can see it is ideological correct, but scale is different and I think wrong. There are problems with normalization, since the results mast be identic. What is wrong in normalization and how to handle it?