sper.m

solution for the Statistical modelling for digital signal processing by hayes

function Px = sper(x,win,M,n1,n2)

%SPER	Spectrum estimation using periodogram smoothing.

%----

%USAGE	Px = sper(x,win,M,n1,n2)

%

%	The spectrum of a process x is estimated using periodogram 

%	smoothing.

%

%	x   : input sequence

%       n1  : starting index, x(n1)

%	n2  : ending index, x(n2)

%	win : The window type 

%       	1 = Rectangular

%		2 = Hamming

%		3 = Hanning

%		4 = Bartlett

%		5 = Blackman

%	M   :  Length of the window

%

%       If n1 and n2 are not specified the periodogram of the entire

%       sequence is computed.

%

%	The smoothed periodogram is returned in Px using a linear scale.

%

%  see also BART, MPER, PER, and WELCH

%

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

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

% "Statistical Digital Signal Processing and Modeling"

% (John Wiley & Sons, 1996).

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



x   = x(:);

if nargin == 3

    n1 = 1;  n2 = length(x);  end;

R  = covar(x(n1:n2),M+1);

r  = [conj(fliplr(R(1,2:M+1))),R(1,1),R(1,2:M+1)];

r'

M  = 2*(M+1)-1;

w  = ones(M,1);

if (win == 2) w = hamming(M);

   elseif (win == 3) w = hanning(M);

   elseif (win == 4) w = bartlett(M);

   elseif (win == 5) w = blackman(M); 

   end;

w

r = r'.*w;

%N  = max(1024,n2-n1+1);

Px = abs(fft(r,1024));

Px(1)=Px(2);

end;