ARMASPEC Computes the spectral density for an AR- or ARMA-model. The process is governed by the system equation A(q) * x(t) = C(q) * sqrt(s2) * e(t) S = armaspec(C,A,s2,n) S = Spectral density. [f1 S1; f2 S2; ... fn Sn] (Frequencies in row 1 and spectral density in row 2.) C = Coefficients in C-polynomials. [1 c_1 ... c_nc] A = Coefficients in A-polynomials. [1 a_1 ... a_na] s2 = Innovation variance. n = Number of calculated values. Example: AR(2)-process. S = armaspec(1,[1 1 0.9],1,500); plot(S(:,1),S(:,2)) Example: ARMA(4,2)-process. S = armaspec([1 0.05 -0.88],[1 -2.06 1.64 -0.98 0.41],4.84e-6,500); plot(S(:,1),S(:,2))
Digital filter frequency response. |
Demo for switching AR(1)-processes. |
001 function [R]=armaspec(C,A,s2,n) 002 003 % ARMASPEC Computes the spectral density for an AR- or ARMA-model. 004 % The process is governed by the system equation 005 % A(q) * x(t) = C(q) * sqrt(s2) * e(t) 006 % 007 % S = armaspec(C,A,s2,n) 008 % 009 % 010 % S = Spectral density. [f1 S1; f2 S2; ... fn Sn] 011 % (Frequencies in row 1 and spectral density in row 2.) 012 % 013 % C = Coefficients in C-polynomials. [1 c_1 ... c_nc] 014 % A = Coefficients in A-polynomials. [1 a_1 ... a_na] 015 % s2 = Innovation variance. 016 % n = Number of calculated values. 017 % 018 % Example: AR(2)-process. 019 % S = armaspec(1,[1 1 0.9],1,500); 020 % plot(S(:,1),S(:,2)) 021 % Example: ARMA(4,2)-process. 022 % S = armaspec([1 0.05 -0.88],[1 -2.06 1.64 -0.98 0.41],4.84e-6,500); 023 % plot(S(:,1),S(:,2)) 024 025 % Copyright (c) 1997 by Pär Johannesson 026 % Toolbox: Rainflow Cycles for Switching Processes V.1.0, 2-Oct-1997 027 028 [H,w]=freqz(C,A,n); 029 R=real(s2*H.*conj(H)); 030 f=w/(2*pi); 031 032 R = [f R]; 033
Comments or corrections to the WAFO group