tune/eq/eq_define_parametric_eq.m

function [z, p, k] = eq_define_parametric_eq(peq, fs)

%%
% Copyright (c) 2016, Intel Corporation
% All rights reserved.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
%   * Redistributions of source code must retain the above copyright
%     notice, this list of conditions and the following disclaimer.
%   * Redistributions in binary form must reproduce the above copyright
%     notice, this list of conditions and the following disclaimer in the
%     documentation and/or other materials provided with the distribution.
%   * Neither the name of the Intel Corporation nor the
%     names of its contributors may be used to endorse or promote products
%     derived from this software without specific prior written permission.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
% POSSIBILITY OF SUCH DAMAGE.
%
% Author: Seppo Ingalsuo <seppo.ingalsuo@linux.intel.com>
%

% Parametric types
PEQ_HP1 = 1; PEQ_HP2 = 2; PEQ_LP1 = 3; PEQ_LP2 = 4;
PEQ_LS1 = 5; PEQ_LS2 = 6; PEQ_HS1 = 7; PEQ_HS2 = 8;
PEQ_PN2 = 9; PEQ_LP4 = 10; PEQ_HP4 = 11;

sp = size(peq);
z = [];
p = [];
k = 1;
for i=1:sp(1)
        type = peq(i,1);
        f = peq(i,2);
        g = peq(i,3);
        Q = peq(i,4);
        if f < fs/2
                a0 = [];
                b0 = [];
                z0 = [];
                p0 = [];
                k0 = [];
                switch peq(i,1)
                        case PEQ_HP1, [z0, p0, k0] = butter(1, 2*f/fs, 'high');
                        case PEQ_HP2, [z0, p0, k0] = butter(2, 2*f/fs, 'high');
                        case PEQ_HP4, [z0, p0, k0] = butter(4, 2*f/fs, 'high');
                        case PEQ_LP1, [z0, p0, k0] = butter(1, 2*f/fs);
                        case PEQ_LP2, [z0, p0, k0] = butter(2, 2*f/fs);
                        case PEQ_LP4, [z0, p0, k0] = butter(4, 2*f/fs);
                        case PEQ_LS1, [b0, a0] = low_shelf_1st(f, g, fs);
                        case PEQ_LS2, [b0, a0] = low_shelf_2nd(f, g, fs);
                        case PEQ_HS1, [b0, a0] = high_shelf_1st(f, g, fs);
                        case PEQ_HS2, [b0, a0] = high_shelf_2nd(f, g, fs);
                        case PEQ_PN2, [b0, a0] = peak_2nd(f, g, Q, fs);
                        otherwise
                                error('Unknown parametric EQ type');
                end
                if length(a0) > 0
                        [z0, p0, k0] = tf2zp(b0, a0);
                end
                if length(k0) > 0
                        z = [z ; z0(:)];
                        p = [p ; p0(:)];
                        k = k * k0;
                end
        end
end
end

function [b, a] = low_shelf_1st(fhz, gdb, fs)
zw = 2*pi*fhz;
w = wmap(zw, fs);
glin = 10^(gdb/20);
bs = [1 glin*w];
as = [1 w];
[b, a] = my_bilinear(bs, as, fs);
end

function [b, a] = low_shelf_2nd(fhz, gdb, fs)
zw = 2*pi*fhz;
w = wmap(zw, fs);
glin = 10^(gdb/20);
bs = [1 w*sqrt(2*glin) glin*w^2];
as = [1 w*sqrt(2) w^2];
[b, a] = my_bilinear(bs, as, fs);
end

function [b, a] = high_shelf_1st(fhz, gdb, fs)
zw = 2*pi*fhz;
w = wmap(zw, fs);
glin = 10^(gdb/20);
bs = [glin w];
as = [1 w];
[b, a] = my_bilinear(bs, as, fs);
end

function [b, a] = high_shelf_2nd(fhz, gdb, fs)
zw = 2*pi*fhz;
w = wmap(zw, fs);
glin = 10^(gdb/20);
bs = [glin w*sqrt(2*glin) w^2];
as = [1 w*sqrt(2) w^2];
[b, a] = my_bilinear(bs, as, fs);
end


function [b, a] = peak_2nd(fhz, gdb, Q, fs)
	% Reference http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt
	A = 10^(gdb/40); % Square root of linear gain
	wc = 2*pi*fhz/fs;
	alpha = sin(wc)/(2*Q);
	b0 = 1 + alpha * A;
	b1 = -2 * cos(wc);
	b2 = 1 - alpha * A;
	a0 = 1 + alpha / A;
	a1 = -2 * cos(wc);
	a2 = 1 - alpha / A;
	b = [b0 / a0 b1 / a0 b2 / a0];
	a = [1 a1 / a0 a2 / a0];
end

function [b, a] = my_bilinear(sb, sa, fs)
if exist('OCTAVE_VERSION', 'builtin')
        [b, a] = bilinear(sb, sa, 1/fs);
else
        [b, a] = bilinear(sb, sa, fs);
end
end

function sw = wmap(w, fs)
t = 1/fs;
sw = 2/t*tan(w*t/2);
end