# nonst_stat

## PURPOSE

Nonstationarity test - continuous process

## SYNOPSIS

function sigma = nonst_stat(data,A,sumV,params)

## DESCRIPTION

     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)

## CROSS-REFERENCE INFORMATION

This function calls:

- mtfftc Multi-taper fourier transform - continuous data
- dpsschk Helper function to calculate tapers and, if precalculated tapers are supplied,
- getparams Helper function to convert structure params to variables used by the

This function is called by:

## SOURCE CODE

    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