How Can I correct amplitude and smoothness of FFT?

Question

I am trying to create 10 individual signals with on-off keying modulation format, add them up to have a final signal, and then take a Fourier transform of that signal. I tried to zero padd the final signal before taking fft so that I can correct amplitude for my spectrum based on this link: Amplitude Estimation and Zero Padding

However, I still do not get amplitude one for frequencies of interest. I am new to both Matlab and signal processing. I do appreciate any help to fix the problems. Below is my code in Matlab:

clc, clear all, close all;
NStep  = 20;        % the number of bits
R   = 20;           % Bit rate (Gbps)
Tr  = 1/R;          % bit period (nanosecond)
x  = randi([0,1],1,NStep);       % Binary information 
N  = length(x);
nb = 100;                        % Digital signal per bit
t  = Tr/nb:Tr/nb:nb*N*(Tr/nb);   % Time period (ns)
Digit = [];
for n = 1:1:NStep
        if x(n) == 1;
            sig = ones(1,nb);
        else x(n) == 0;
            sig = zeros(1,nb);
        end
        Digit = [Digit sig];
    end

subplot(2,1,1)
plot(t,Digit);
xlabel('Time (ns)');
ylabel('Amplitude');
%% fft
lpad = length(Digit); 
xdft = fft(Digit,lpad);
xdft = xdft(1:lpad/2+1);
xdft = xdft/length(Digit);
xdft(2:end-1) = 2*xdft(2:end-1);          
fs = 1/(Tr/nb);
freq = 0:fs/lpad:fs/2;
subplot(2,1,2) 
plot(freq,abs(xdft))
xlabel('Frequency (GHz)');
ylabel('Amplitude');

Answer 1

The expected spectrum for one stream of on-off keying modulation would be the given by the Fourier Transform of the base pulse (a rectangular pulse in this case) assuming random data and sufficient number of samples. In the example used by the OP there are an insufficient number of samples to provide the statistical distribution representing "random data". Additionally note that FFT scales by the total number of samples $N$, so to normalize we would divide the result by $N$. For on/off keying, we expect to have on average half the number of samples as "1" and the other half as "0", so without normalization the magnitude of the FFT should be $N$ and go down as a Sinc function given the Fourier Transform of a rectangular pulse is a Sinc. I show this with the example code below:

N = 1000;
data = sign(rand(N,1)*2-1);
oversamp = 10;
modulated = data * ones(1, 10);
modout = reshape(modulated',1, N*10);
fout =  fft(modout, 2**18)./N;
freqaxis = [-2^17+1: 2^17]/2^18;
figure
plot(freqaxis, fftshift(20*log10(abs(fout))))

Note: the spectrum plotted is that with 10 samples per symbol, and the result is a "Dirichlet Kernel" rather than a true Sinc function. The Dirichlet Kernel approaches a Sinc as the number of samples per symbol goes to infinity.