Envelopes in Matlab

• In a system such as Matlab, a linear line segment envelope can be computed from the expression $y(t) = m (t - t_0) + y_0$, where $m$ is the line slope, $t_0$ is the initial time value and $y_0$ is the value of $y$ at $t_0$.

  fs = 44100;
  Ts = 1 / fs;
  t = [2 5]; % start and end times in seconds
  tvals = t(1):Ts:t(2);
  y = [4 2];
  m = diff( y ) / diff( t )
  plot( tvals, y(1)+m*(tvals-t(1)) )
  xlabel('Time (seconds)');
  ylabel('Amplitude');
  

• Another option is to use the linspace function, which takes arguments of y1, y2, n. Given the t and y values above, the envelope could be produced as: env = linspace( y(1), y(2), abs(diff(t))*fs+1 );

• The Matlab scripts curve.m and asymp.m demonstrate the implementation of exponential/logarithmic and asymptotic envelope segments.