Sampling a signal

• To sample a signal in MATLAB, generate a time vector at the appropiate rate, and use this to generate the signal. Plot using the stem function. For example:

  % Sample the sinusoid x = sin(2 pi f t), where f = 2 kHz.
  % Let x1 be the signal sampled at 10 kHz.
  % Let x2 be the signal sampled at 3 kHz.
  
  f = 2000;
  T = 1/f;
  tmin = 0;
  tmax = 5*T;             % Plot 5 cycles
  dt1 = 1/10000;
  dt2 = 1/3000;
  t1 = tmin:dt1:tmax;
  t2 = tmin:dt2:tmax;
  x1 = sin(2*pi*f*t1);
  x2 = sin(2*pi*f*t2);
  subplot(211)
  stem(t1,x1);
  subplot(212)
  stem(t2,x2);
  

• It is useful to plot the continuous time signal on the same plot. All signals in MATLAB are discrete-time, but they will look like continuous-time signals if the sampling rate is much higher than the Nyquist rate:

  % Sample the sinusoid x = sin(2 pi f t), where f = 2 kHz, and plot the sampled
  % signals over the continuous-time signal.
  % Let x1 be the signal sampled at 10 kHz.
  % Let x2 be the signal sampled at 3 kHz.
  
  f = 2000;
  T = 1/f;
  tmin = 0;
  tmax = 5*T;
  dt = T/100;
  dt1 = 1/10000;
  dt2 = 1/3000;
  t = tmin:dt:tmax;
  t1 = tmin:dt1:tmax;
  t2 = tmin:dt2:tmax;
  x = sin(2*pi*f*t);
  x1 = sin(2*pi*f*t1);
  x2 = sin(2*pi*f*t2);
  subplot(211)
  plot(t,x,'r');
  hold on
  stem(t1,x1);
  subplot(212)
  plot(t,x,'r');
  hold on
  stem(t2,x2);