Delay Vector Variance method for real and complex signals
USAGE: C = dvv (X, m, Nsub, nd, Ntv)
Input:
X original real-valued or complex time series
m delay embedding dimension
Ntv number of points on horizontal axes
Nsub number of reference DVs to consider
nd Span over which to perform DVV
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Complex Valued Nonlinear Adaptive Filtering toolbox for MATLAB
Supplementary to the book:
"Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models"
by Danilo P. Mandic and Vanessa Su Lee Goh
(c) Copyright Danilo P. Mandic 2009
http://www.commsp.ee.ic.ac.uk/~mandic
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This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You can obtain a copy of the GNU General Public License from
http://www.gnu.org/copyleft/gpl.html or by writing to
Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
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...........................................0001 % Delay Vector Variance method for real and complex signals 0002 % 0003 % 0004 % USAGE: C = dvv (X, m, Nsub, nd, Ntv) 0005 % 0006 % Input: 0007 % X original real-valued or complex time series 0008 % m delay embedding dimension 0009 % Ntv number of points on horizontal axes 0010 % Nsub number of reference DVs to consider 0011 % nd Span over which to perform DVV 0012 % ........................................... 0013 % 0014 % Complex Valued Nonlinear Adaptive Filtering toolbox for MATLAB 0015 % Supplementary to the book: 0016 % 0017 % "Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models" 0018 % by Danilo P. Mandic and Vanessa Su Lee Goh 0019 % 0020 % (c) Copyright Danilo P. Mandic 2009 0021 % http://www.commsp.ee.ic.ac.uk/~mandic 0022 % 0023 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0024 % This program is free software; you can redistribute it and/or modify 0025 % it under the terms of the GNU General Public License as published by 0026 % the Free Software Foundation; either version 2 of the License, or 0027 % (at your option) any later version. 0028 % 0029 % This program is distributed in the hope that it will be useful, 0030 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0031 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0032 % GNU General Public License for more details. 0033 % 0034 % You can obtain a copy of the GNU General Public License from 0035 % http://www.gnu.org/copyleft/gpl.html or by writing to 0036 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0037 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0038 % ........................................... 0039 function data = dvv (X, m, Nsub, nd, Ntv) 0040 0041 % Default parameters 0042 if (nargin<1) 0043 error('Not enough Input arguments'); 0044 end 0045 if (nargin<2) 0046 m = 4; 0047 end 0048 if (nargin<3) 0049 Nsub = 200; 0050 end 0051 if (nargin<4) 0052 nd = 2.0; 0053 end 0054 if (nargin<5) 0055 Ntv = 25*nd; 0056 end 0057 0058 % Initial Conditions 0059 N = length(X); % Length of input vector 0060 tau = 1; % Time delay parameter 0061 d = zeros(N-m*tau, Nsub); 0062 y = zeros(Ntv,1); 0063 count = 0; 0064 acc = 0; 0065 0066 0067 % Makes input vector X a column vector 0068 if (size(X,2)>size(X,1)) 0069 X = X'; 0070 end 0071 0072 % Generate Nsub subset from existing DV's, randomly 0073 temp = randperm (N - m*tau); 0074 ref = temp(1:Nsub) + m*tau; 0075 0076 % Computes the pair wise distances b/w reference DV's and all DV's 0077 for i = 1:Nsub 0078 for j = m*tau+1:N 0079 d(j-m*tau,i) = norm (X(ref(i)-m*tau:tau:ref(i)-tau) - X(j-m*tau:tau:j-tau)); 0080 if (ref(i) ~= j) 0081 acc = acc + d(j-m*tau,i); 0082 count = count + 1; 0083 end 0084 end 0085 end 0086 0087 % Mean and std variation calculation of input data 0088 avg = acc/count; 0089 count = 0; 0090 acc = 0; 0091 for i = 1:Nsub 0092 for j = m*tau + 1:N 0093 if (ref(i) ~= j) 0094 acc = acc + (d(j-m*tau,i)-avg).^2; 0095 end 0096 end 0097 end 0098 variance = sqrt(acc/(count-1)); 0099 0100 % Calculates the range vector consisting of Ntv equally spaced regions 0101 n = (1:Ntv)-1; 0102 rd = avg-nd*variance + (2*nd*variance*n)/(Ntv-1); 0103 0104 % Creates sets of DV's, for each ref element of subset and value rd, which have norms closer than distance rd to ref 0105 for n = 1:length(rd) 0106 0107 if (rd(n)>0) 0108 0109 tot = 0; 0110 count = 0; 0111 0112 for k=1:Nsub 0113 0114 IND = find(d(:,k) <= rd(n)) + m*tau; 0115 IND = IND(IND~=k); 0116 0117 0118 % Only those variance values are considered for which the corresponding 0119 % sets have atleast 30 DVs 0120 if (length(IND) >= 30) 0121 tot = tot + var(X(IND)); 0122 count = count+1; 0123 end 0124 end 0125 if (~count) 0126 y(n) = NaN; 0127 else 0128 y(n) = tot/(count*var(X)); 0129 end 0130 0131 else 0132 y(n) = NaN; 0133 end 0134 0135 end 0136 0137 % Horizontal axis 0138 T = (rd'-avg)/variance; 0139 0140 % DVV Output 0141 data = [T y];