pdfb_ang.m

PDTDFB toolbox The filter bank is described in: The Shiftable Complex Directional Pyramid—Pa

function ang= pdfb_ang(insub, nlev)
% PDFB_ANG Determine the dfb subband that the angle fall into
%       ang = pdfb_ang(insub, nlev)
% 
% Returning value ang is from 3pi*4 to -pi/4 to make the range of value
% change continuosly from band 1 to 2^nlev
% Input:
%   insub:  index of the subband from 1 to 2^nlev
%   nlev:   2^nlev is the number of direction band
%
% Output:
%   ang:	the angle of direction of the band in radian
%
% Note:
% Note: An important thing to remember is that the ang is limited to -pi/2
% to pi/2, but the actual angle of the complex filter is from -pi to pi.
% This is because the complex filter contained a imaginary anti-symmetric
% component. We consider the direction of the impulse responses is that if
% we go in the positive direction, the right hand side will corresponds to
% the positive (larger than zero) of an antisymmetric wave (forexample,
% sine function)
%                               ^ pi/2
%                        \      |      /band 2^(N-1)  
%                          \    |    /    
%                            \  |  / 
%                              \|/   +  band 2^(N-1)+2^(N-2)
%                               |----------------->
%                               |\   -
%                               |  \  
%                               |    \  band 2^N - 1 
%                               |   b0 \ 
%                               |-pi/2
% See also: ANG_PDFB

% number of all sb 
n4 = 2^(nlev-2);

% artang value of the smallest angle
atanstrt = 1/(n4*2);
% artang step from adjacent subband
atanstep = 1/(n4);

atanv = atanstrt:atanstep:atanstrt+atanstep*(n4-1);
% correspoding angle value in radian
angsb = atan(atanv);
angsbrev = fliplr(angsb);

% angle of the four group of direction subbands
aq1 = angsbrev + pi/2;
aq2 = -fliplr(angsbrev - pi/2);
aq3 = angsbrev;
aq4 = -fliplr(aq3);
aq = [aq1, aq2, aq3, aq4];

ang = aq(insub);