spsvd

 Space frequency SVD of input data - continuous processes
 Usage: [sv,sp,fm] = spsvd(data,params,mdkp)
 Inputs:
 data       (data matrix in timexchannels form)-required
       params      structure containing parameters - params has the
       following fields: tapers, Fs, fpass, pad
           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

            Fs             (sampling frequency) -- optional. Defaults to 1.
           fpass       (frequency band to be used in the calculation in the form
                                   [fmin fmax])- optional. 
                                   Default all frequencies between 0 and Fs/2
            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.
 mdkp       (number of dimensions to be kept)-optional. Default is the
               maximum possible modes determined by taper parameters

 Outputs:
 sv sp fm  : singular values, space modes, frequency modes

0001 function [sv,sp,fm] = spsvd(data,params,mdkp)
0002 % Space frequency SVD of input data - continuous processes
0003 % Usage: [sv,sp,fm] = spsvd(data,params,mdkp)
0004 % Inputs:
0005 % data       (data matrix in timexchannels form)-required
0006 %       params      structure containing parameters - params has the
0007 %       following fields: tapers, Fs, fpass, pad
0008 %           tapers : precalculated tapers from dpss or in the one of the following
0009 %                    forms:
0010 %                   (1) A numeric vector [TW K] where TW is the
0011 %                       time-bandwidth product and K is the number of
0012 %                       tapers to be used (less than or equal to
0013 %                       2TW-1).
0014 %                   (2) A numeric vector [W T p] where W is the
0015 %                       bandwidth, T is the duration of the data and p
0016 %                       is an integer such that 2TW-p tapers are used. In
0017 %                       this form there is no default i.e. to specify
0018 %                       the bandwidth, you have to specify T and p as
0019 %                       well. Note that the units of W and T have to be
0020 %                       consistent: if W is in Hz, T must be in seconds
0021 %                       and vice versa. Note that these units must also
0022 %                       be consistent with the units of params.Fs: W can
0023 %                       be in Hz if and only if params.Fs is in Hz.
0024 %                       The default is to use form 1 with TW=3 and K=5
0025 %
0026 %            Fs             (sampling frequency) -- optional. Defaults to 1.
0027 %           fpass       (frequency band to be used in the calculation in the form
0028 %                                   [fmin fmax])- optional.
0029 %                                   Default all frequencies between 0 and Fs/2
0030 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
0031 %                    -1 corresponds to no padding, 0 corresponds to padding
0032 %                    to the next highest power of 2 etc.
0033 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
0034 %                       to 512 points, if pad=1, we pad to 1024 points etc.
0035 %                       Defaults to 0.
0036 % mdkp       (number of dimensions to be kept)-optional. Default is the
0037 %               maximum possible modes determined by taper parameters
0038 %
0039 % Outputs:
0040 % sv sp fm  : singular values, space modes, frequency modes
0041 
0042 
0043 if nargin < 1; error('Need data'); end;
0044 if nargin < 2 || isempty(params); params=[]; end;
0045 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
0046 clear err trialave params
0047 [N,NCHAN]=size(data);
0048 tapers=dpsschk(tapers,N,Fs);
0049 nfft=max(2^(nextpow2(N)+pad),N);% number of points in fft
0050 [N,K]=size(tapers);
0051 if nargin<3 || isempty(mdkp); mdkp=min(K,NCHAN);
0052 elseif mdkp > min(K,NCHAN); error('mdkp has to be less than both K and NCHAN');end;
0053 
0054 tvec=(1:N)';
0055 tvec=repmat(tvec,[1 K]);
0056 tvec=tvec*2*pi*i;
0057 f=getfgrid(Fs,nfft,fpass);
0058 nf=length(f);
0059 sp=zeros(NCHAN,nf,mdkp);
0060 sp=sp+i*sp;
0061 fm=zeros(K,nf,mdkp);
0062 fm=fm+i*fm;
0063 sv=zeros(nf,min([K,NCHAN]));
0064 for j=1:nf 
0065 %     for k=1:K
0066 %       proj(:,k)=tapers(:,k).*exp(-f0*tvec');
0067 %     end
0068     proj=tapers.*exp(-f(j)*tvec);
0069     tmp=data'*proj; % projected data
0070     [u,s,v]= svd(tmp,0); % svd
0071     for mk=1:mdkp, 
0072       sp(:,j,mk)=u(:,mk)';
0073       fm(:,j,mk)=v(:,mk)';
0074     end  
0075     sv(j,:)=diag(s);
0076 end;