I am performing some analysis on a sine wave, and I noticed something peculiar. When I introduced a single sample impulse randomly at any point in the sine frame, the FFT failed to locate it. Intuitively, an Impulse's FFT should be a Sine Wave, but I didn't get anything. In fact, I will say information was lost. Why is that the case?

![enter image description here](https://i.stack.imgur.com/h1LVA.jpg)

To be absolutely clear about the code that generated this:

```
Fs=10e3; %Specify Sampling Frequency 
Ts=1/Fs; %Sampling period. 
Ns= 1024; %Number of time samples to be plotted. 
temp = Ts*(Ns-1);
t=[0:Ts:Ts*(Ns-1)]; %Make time array that contains Ns elements 
%t = [0, Ts, 2Ts, 3Ts,..., (Ns-1)Ts] 
f1= 60; 
f2=1000; 
f3=2000; 
f4=3200; 

x1=sin(2*pi*f1*t (1 : size(t, 2)/2)); %create sampled sinusoids at different frequencies 
x1(1, 400) = 5;
x2=cos(2*pi*f2*t (size(t, 2)/2 + 1: size(t, 2))) ; 

x = [x1 x2];

xfftmag=(abs(fft(x)));
xfftmagh=xfftmag(1:length(xfftmag)/2); 
%Plot only the first half of FFT, since second half is mirror imag 
%the first half represents the useful range of frequencies from 
%0 to Fs/2, the Nyquist sampling limit. 
f=[1:1:length(xfftmagh)]*Fs/Ns; %Make freq array that varies from 
%0 Hz to Fs/2 Hz. 

[ca, cd] = swt(x, 1, 'haar');

```