Plotting a continuous-time signal and its spectrum

• Consider the signal x(t) = e^-|t|. Its spectrum is

                 2
       X(f) = ------------
                          2
              1 + (2 pi f)
  

  The following MATLAB program will plot x(t) and X(f) (in dB).

  tmax = 5;          % 5 time constants
  t = -tmax:.001:tmax;
  x = exp(-abs(t));
  subplot(211)
  plot(t,x)
  xlabel('t (sec)')
  ylabel('x(t)')
  title('x(t) = exp(-|t|)');
  
  f = -5:.001:5;
  X = 2./(1+(2*pi*f).^2);
  subplot(212)
  plot(f,20*log10(abs(X)))
  xlabel('f (Hz)')
  ylabel('|X(f)| (dB)')