A Couple Examples

• To create a simple sinusoidal signal:

  fs = 44100;                    % sampling rate
  T = 1/fs;                      % sampling period
  t = [0:T:0.25];                % time vector
  
  f1 = 50;                       % frequency in Hertz
  omega1 = 2*pi*f1;              % angular frequency in radians
  
  phi = 2*pi*0.75;               % arbitrary phase offset = 3/4 cycle
  x1 = cos(omega1*t + phi);      % sinusoidal signal, amplitude = 1
  
  plot(t, x1);                   % plot the signal
  xlabel('Time (seconds)');
  ylabel('x1');
  title('Simple Sinusoid');
  
  sound(0.9*x1, fs);             % play the signal
  

• To create a more complex signal composed of many sinusoids:

  phi = 2 * pi * 0.25;           % 1/4 cycle phase offset
  x1 = cos(omega1*t + phi);      % sinusoidal signal, amplitude = 1
  x2 = cos(2*pi*150*t + phi)/3;  % sinusoidal signal, amplitude = 1/3
  x3 = cos(2*pi*250*t + phi)/5;  % sinusoidal signal, amplitude = 1/5
  x4 = cos(2*pi*350*t + phi)/7;  % sinusoidal signal, amplitude = 1/7
  x5 = cos(2*pi*450*t + phi)/9;  % sinusoidal signal, amplitude = 1/9
  
  xcomplex = x1 + x2 + x3 + x4 + x5;
  
  plot(t, xcomplex);
  xlabel('Time (seconds)');
  ylabel('xcomplex');
  title('More Complex Signal');
  
  sound(0.9*xcomplex, fs);       % play the signal