convm.m

solution for the Statistical modelling for digital signal processing by hayes

function X = convm(x,p)

%CONVM	Generates a convolution matrix

%-----

%USAGE	X = convm(x,p) 

%

%	Given a vector x of lenght N, an N+p-1 by p convolution 

%	matrix of the following form is generated

%

%              |  x(0)  0      0     ...      0    |

%              |  x(1) x(0)    0     ...      0    |

%              |  x(2) x(1)   x(0)   ...      0    |

%         X =  |   .    .      .              .    |

%              |   .    .      .              .    |

%              |   .    .      .              .    |

%              |  x(N) x(N-1) x(N-2) ...  x(N-p+1) |

%	       |   0   x(N)   x(N-1) ...  x(N-p+2) |

%              |   .    .      .              .    |

%              |   .    .      .              .    |

%	       |   0    0      0     ...    x(N)   |

%

%

%---------------------------------------------------------------

% copyright 1996, by M.H. Hayes.  For use with the book 

% "Statistical Digital Signal Processing and Modeling"

% (John Wiley & Sons, 1996).

%---------------------------------------------------------------



N    = length(x)+2*p-2;

x    = x(:);

xpad = [zeros(p-1,1);x;zeros(p-1,1)];

for  i=1:p

     X(:,i)=xpad(p-i+1:N-i+1);

     end;