samer@32: function map=specbasis(edges,M)
samer@32: % specbasis - Create frequency mapping matrix
samer@32: %
samer@32: % as_fmap ::
samer@32: %    [[L-1]]    ~ 'array of L-1 bin edge frequencies, in FT bins',
samer@32: %    M:natural  ~ 'number of bins in linear-freq spectrum'
samer@32: % ->
samer@32: %    [[L,M]]    ~ 'L-by-M sparse array'.
samer@33: % 
samer@33: % Converts a filterbank specification into a sparse matrix for
samer@33: % mutliplying with a linear-frequency spectrogram.
samer@32: %
samer@32: % Note, frequencies must measured in bins of the target spectrum,
samer@32: % Also, the first and last of the L bands are catch-alls which
samer@32: % get all energy below the bottom edge and above the top edge
samer@32: % respectively. If, eg, the bottom edge is 0, then the bottom
samer@32: % band will be empty.
samer@32: 
samer@33: E=repmat([0; edges(:); M-1],1,M);
samer@33: I=repmat(0:M-1,length(edges)+1,1);
samer@33: map=sparse(phi(E(2:end,:)-I)-phi(E(1:end-1,:)-I));
samer@33: map=map.*(map>8e-15); % squeeze out more small values
samer@33: map(:,2:end-1)=map(:,2:end-1)/2; % make up for top and bottom bins
samer@32: 
samer@32: %                                     ____
samer@32: % this is piecewise linear ramp : ___/
samer@32: % It models the response of an FFT bin to a band edge as the edge 
samer@32: % moves across the frequency range. The response of a bin to a
samer@32: % band is computed as the sum of responses due to the left and
samer@32: % right edges, ie, for the ith FT bin, 
samer@32: %    response=phi(e1-i)-phi(e2-i)
samer@32: % where e1 and e2 are the lower and upper edges of the band
samer@32: function y=phi(x), y=abs(x+0.5)-abs(x-0.5);
samer@32: