Uniform noise signal Good afternoon. I have some heart monitor data that I am attempting to analyze. I have been given time between the peaks (in milliseconds), and have attempted to reverse-engineer a signal from this using the following code.

clc;
clear all;
%Sampling frequency
Fs = 250;
%total data time (s)
ts = xlsread('12_RR_1.xlsx','G:G');
%total data time (ms)
%total_time = xlsread('12_RR.csv.xlsx','I:I');
%Point in time where there is a max point
xn = xlsread('12_RR_1.xlsx','H:H');
xnt = size(xn);


t = 1:ts;
time = transpose(t);


for i = 1:ts
    for j = 1:xnt(1,1)
        z(i,j) = xn(j,1);
    end
        i = i+1;
        j = j+1;
end

for i_2= 1:97484
    for j = 1:xnt(1,1)
   if time(i_2,1) == z(i_2,j)
       z_raw(i_2,j) = 1;
   else
       z_raw(i_2,j) = 0;
   end
    end
    i_2 = i_2+1;
   j = j+1;
end

 peaks = sum(z_raw,2);
 Peaks = abs(peaks);
  N = length(peaks);



 subplot(2,1,1)
 plot(t,Peaks)
 title('Raw Data')
 subplot(2,1,2)
 plot(t/Fs,fft(Peaks,ts))
 title('FFT')


This produces a binary signal where y=1 if a peak is detected and y=0 if it is not. However, when I attempted to take the FFT of this it returns a signal with weirdly uniform noise, as shown below.



What's going on--why does a seemingly low-frequency signal have a uniform frequency response? What can I do to my original data (the time between heart impulses) to extract more meaningful information and get a more realistic FFT (high amp low freq data with small amp high freq data)
Your signal is a superposition of fairly widely spaced impulses. Each impulse by itself has a flat magnitude spectrum and the intervals between impulses are only pseudo periodic so the phase response superpositions are effectively incoherent. The problem isn't your FFT, it is your signal model. 

An actual ECG is much smoother. If you expect to see a predominant frequency at around 1Hz, the signal would look like a sine wave of around 1 Hz, not a sequence of isolated spikes.  

You probably really want to measure the time intervals between spikes directly in the the time domain.