Matlab Notes-Discrete-time Signals and Systems

Discrete-time Signals

Unit Impluse Signal

• 

• Function-impseq.m

  % The sequence will range at n1 to n2
  % When n=n0 => x=1
  function [x, n]=impseq(n0,n1,n2)
  n=n1:n2;
  x=((n-n0)==0); %if n-n0==0 then x=1 else x=0
  end

• Test Code-test.m

  [x, n]=impseq(0, -1, 5);
  x_plot=stem(n, x, 'b', 'filled');
  set(x_plot, 'markersize', 4);
  xlabel("n"); ylabel("x"); title('plot of x[n] when -1<n<5');

• Result

  

Unit Setp Sequence

• 

• Function-uniseq.m

  % The sequence will range at n1 to n2
  % When n>=n0 => x=1 
  function [x, n] = uniseq(n0, n1, n2)
  n=n1:n2; 
  x=(n-n0>=0); % If n-n0>=0 => x=1, else => x=0
  end

• Test Code-test.m

  [x, n] = uniseq(2, -1, 5);
  x_plot = stem(n, x, 'b', 'filled');
  set(x_plot, 'markersize', 4);
  xlabel("n"); ylabel("x"); title('plot of x[n] when -1<n<5');

• Result

  

Real-valued Exponential Sequence

• 

• Test Code-test.m

  n=0:10;
  x=2.^(n); % To create a sequence '.' is needed
  x_plot=stem(n,  x, 'filled', 'b');
  set(x_plot, 'markersize', 4); %chagne the size of the circle
  xlabel("n"); ylabel("x"); title('plot of x[n] when 0<n<10');

• Result

  

Complex-valued Exponential Sequence

• 

  • Where σ produces an attenuation (if <0) or amplification (if >0) and is the frequency in radians.

• Test Code-test.m

  n=-8:8;
  w=0.5*pi;
  x=exp(j*w*n);
  subplot(2, 1, 1);
  x_plot=stem(n, real(x), 'filled', 'b');
  title("real part of x");
  xlabel("n"); ylabel("x");
  subplot(2, 1, 2);
  y_plot=stem(n, imag(x), 'filled', 'r');
  title("image part of x");
  xlabel("n"); ylabel("x");

• Result

  

Sinusodial Sequence

• 

  • Where A is an amplitude, is the frequency in radians and is the phase in radians .

• Test Code-test.m

  n=-8:8;
  w=0.5*pi;
  p1=0*pi;
  p2=0.5*pi;
  A=2;
  x=A*cos(w*n+p1);
  y=A*cos(w*n+p2);
  subplot(2, 1, 1);
  x_plot=stem(n, x, "filled", 'b');
  title("with no phase");
  xlabel("n"); ylabel("x");
  subplot(2, 1, 2);
  y_plot=stem(n, y, "filled", 'r');
  title("with phase of 0.5*pi");
  xlabel("n"); ylabel("x");

• Result

  

Random Sequence

• The randn(1,N) generates a length N Gaussian random sequence with mean 0 and variance 1.

• Test Code-test.m

  x=rand(1,10);
  n=1:10;
  x_plot=stem(n, x, "filled", 'b');
  xlabel("n"); ylabel("random x");
  title("random sequence");

• Result