How to plot simple fft of a shifted time series?

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I am trying to understand basic fft functions of a shifted time series and my graphs are not appearing as I expect them to:
dt = 0.01; % time interval N_ts = 256; % number of time data Td_ts = 2.*(N_ts-1)*dt; % duration t_ts = 0:dt:Td_ts; % define time axis x_ts = zeros(1, length(t_ts)); %Initialize x_ts2 = zeros(1, length(t_ts)); %Initialize t0 = 100; t1 = 156; x_ts(t0)= 1/dt; % time shift of x(t+t0) x_ts2(t1) = 1/dt; % time shift of x(t-t0)
nfft_ts = 511; % Length of FFT X2_ts = fft(x_ts2,nfft_ts)*dt; % Take fft, padding with zeros so that Length(x) is equal to nfft
amp2 = abs(X2_ts); % Take the magnitude of fft of x phase2 = angle(X2_ts); % Take angle
figure(5); plot(t_ts,X2_ts); title('Built-In FFT'); xlabel('Time (s)'); ylabel('X(t)');

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