nonst_stat

 Nonstationarity test - continuous process

 Usage:

 sigma=nonst_test(data,A,sumV,params)
 Input: 
 Note units have to be consistent. See chronux.m for more information.
       data (1d array in samples) -- required
       A   quadratic coefficient matrix - (Compute this separately since
       the computation is time consuming - [A,sumV]=quadcof(N,NW,order). order
       has to < 4NW.)
       sumV   sum of the quadratic inverse basis vectors 
       params: structure with fields tapers, pad, Fs, fpass, err, trialave
       -optional
           tapers : precalculated tapers from dpss or in the one of the following
                    forms: 
                    (1) A numeric vector [TW K] where TW is the
                        time-bandwidth product and K is the number of
                        tapers to be used (less than or equal to
                        2TW-1). 
                    (2) A numeric vector [W T p] where W is the
                        bandwidth, T is the duration of the data and p 
                        is an integer such that 2TW-p tapers are used. In
                        this form there is no default i.e. to specify
                        the bandwidth, you have to specify T and p as
                        well. Note that the units of W and T have to be
                        consistent: if W is in Hz, T must be in seconds
                        and vice versa. Note that these units must also
                        be consistent with the units of params.Fs: W can
                        be in Hz if and only if params.Fs is in Hz.
                        The default is to use form 1 with TW=3 and K=5

            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...). 
                    -1 corresponds to no padding, 0 corresponds to padding
                    to the next highest power of 2 etc.
                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
                       to 512 points, if pad=1, we pad to 1024 points etc.
                       Defaults to 0.
           Fs   (sampling frequency) - optional. Default 1.
 Output:
       sigma   (nonstationarity index Thomson, 2000)

0001 function sigma = nonst_stat(data,A,sumV,params)
0002 
0003 % Nonstationarity test - continuous process
0004 %
0005 % Usage:
0006 %
0007 % sigma=nonst_test(data,A,sumV,params)
0008 % Input:
0009 % Note units have to be consistent. See chronux.m for more information.
0010 %       data (1d array in samples) -- required
0011 %       A   quadratic coefficient matrix - (Compute this separately since
0012 %       the computation is time consuming - [A,sumV]=quadcof(N,NW,order). order
0013 %       has to < 4NW.)
0014 %       sumV   sum of the quadratic inverse basis vectors
0015 %       params: structure with fields tapers, pad, Fs, fpass, err, trialave
0016 %       -optional
0017 %           tapers : precalculated tapers from dpss or in the one of the following
0018 %                    forms:
0019 %                    (1) A numeric vector [TW K] where TW is the
0020 %                        time-bandwidth product and K is the number of
0021 %                        tapers to be used (less than or equal to
0022 %                        2TW-1).
0023 %                    (2) A numeric vector [W T p] where W is the
0024 %                        bandwidth, T is the duration of the data and p
0025 %                        is an integer such that 2TW-p tapers are used. In
0026 %                        this form there is no default i.e. to specify
0027 %                        the bandwidth, you have to specify T and p as
0028 %                        well. Note that the units of W and T have to be
0029 %                        consistent: if W is in Hz, T must be in seconds
0030 %                        and vice versa. Note that these units must also
0031 %                        be consistent with the units of params.Fs: W can
0032 %                        be in Hz if and only if params.Fs is in Hz.
0033 %                        The default is to use form 1 with TW=3 and K=5
0034 %
0035 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
0036 %                    -1 corresponds to no padding, 0 corresponds to padding
0037 %                    to the next highest power of 2 etc.
0038 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
0039 %                       to 512 points, if pad=1, we pad to 1024 points etc.
0040 %                       Defaults to 0.
0041 %           Fs   (sampling frequency) - optional. Default 1.
0042 % Output:
0043 %       sigma   (nonstationarity index Thomson, 2000)
0044 
0045 
0046 if nargin < 1; error('Need data'); end;
0047 if nargin < 2; params=[]; end;
0048 
0049 order = length(A);
0050 N = length(data);
0051 %nfft=max(2^(nextpow2(N)+pad),N);
0052 [tapers,pad,Fs]=getparams(params);
0053 tapers=dpsschk(tapers,N,Fs); % check tapers
0054 
0055 alpha=zeros(1,order);
0056 for j=1:order
0057   alpha(j) = trace(squeeze(A(:,:,j))*squeeze(A(:,:,j)));
0058 end;
0059 
0060 tmp=mtfftc(data,tapers,N,Fs);
0061 %tmp=mtfftc(data,tapers,nfft,Fs);
0062 sigma = zeros(length(data),1);
0063 % Pbar = sum(abs(tmp).^2,2)./sum(weights.^2,2);
0064 Pbar=mean(abs(tmp).^2,2);
0065 for ii=1:order
0066   a0=real(sum(tmp'.*(squeeze(A(:,:,ii))*tmp.')))'/alpha(ii);
0067   sigma=sigma+alpha(ii)*(a0./Pbar-sumV(ii)).^2;
0068 end;
0069