function [leak] = interactionMatrix(G,gw,wg,wc,bw)
% interactionMatrix.m
%
% Compute the interaction matrix of a cascade graphic equalizer containing
% the leak factors to account for the band interaction when assigning
% filter gains. All filters are Orfanidis peak/notch filters with
% adjustable bandwidth gain.
%
% Input parameters:
% G = Linear gain at which the leakage is determined
% gw = Gain factor at bandwidth (0.5 refers to db(G)/2)
% wg = Command frequencies i.e. filter center frequencies (in rad/sample)
% wc = Design frequencies (rad/sample) at which leakage is computed
% bw = Bandwidth of filters in radians
%
% Output:
% leak = N by M matrix showing how the magnitude responses of the
% band filters leak to the design frequencies. N is determined from the
% length of the array wc (number of design frequencies) whereas M is
% determined from the length of wg (number of filters)
%
% Uses pareq.m
%
% Written by Vesa Valimaki, Espoo, Finland, 12 April 2016
% Modified by Juho Liski, Espoo, Finland, 26 September 2016
%
% Aalto University, Dept. of Signal Processing and Acoustics
M = length(wg); % The number of center frequencies (filters)
N = length(wc); % The number of design frequencies
leak = zeros(M,N); % Initialize interaction matrix
Gdb = db(G); % Convert linear gain factor to dB
Gdbw = gw*Gdb; % dB gain at bandwidth
Gw = 10.^(Gdbw/20); % Convert to linear gain factors
% Estimate leak factors of peak/notch filters
for m = 1:M; % Filters
[num,den] = pareq(G(m), Gw(m), wg(m), bw(m)); % Parametric EQ filter
H = freqz(num,den,wc); % Evaluate response at wc frequencies
Gain = db(H)/Gdb(m); % Normalized interference (Re 1 dB)
leak(m,:) = abs(Gain); % Store gain in a matrix
end
end