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Merge pull request #61 from singalsu/fix_matlab_iir_eq_proposal 

EQ Tool: Fix compatibility with Matlab and improve accuracy of IIR filters
This commit is contained in:
Liam Girdwood 2018-08-30 12:47:55 +01:00 committed by GitHub
parent 41861aac37 206deaf457
commit eddca597ae
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GPG Key ID: 4AEE18F83AFDEB23
10 changed files with 148 additions and 85 deletions
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15
tune/eq/eq_compute.m
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@ -42,9 +42,9 @@ eq = preprocess_responses(eq);
%% Define target (e.g. speaker) response as parametric filter. This could also
% be numerical data interpolated to the grid.
if length(eq.parametric_target_response) > 0
[eq.b_t, eq.a_t] = eq_define_parametric_eq( ...
[eq.t_z, eq.t_p, eq.t_k] = eq_define_parametric_eq( ...
eq.parametric_target_response, eq.fs);
eq.t_db = eq_compute_response(eq.b_t, eq.a_t, eq.f, eq.fs);
eq.t_db = eq_compute_response(eq.t_z, eq.t_p, eq.t_k, eq.f, eq.fs);
end
if isempty(eq.t_db)
@ -64,16 +64,15 @@ eq.err_db = eq.t_db - eq.m_db;
%% Parametric IIR EQ definition
if eq.enable_iir
[eq.b_p, eq.a_p] = eq_define_parametric_eq(eq.peq, eq.fs);
if length(eq.b_p) > 2*eq.iir_biquads_max+1
[eq.p_z, eq.p_p, eq.p_k] = eq_define_parametric_eq(eq.peq, eq.fs);
if max(length(eq.p_z), length(eq.p_p)) > 2*eq.iir_biquads_max
error('Maximum number of IIR biquads is exceeded');
end
else
eq.b_p = 1;
eq.a_p = 1;
[eq.p_z, eq.p_p, eq.p_k] = tf2zp(1, 1);
end
[eq.iir_eq_db, eq.iir_eq_ph, eq.iir_eq_gd] = eq_compute_response(eq.b_p, ...
eq.a_p, eq.f, eq.fs);
[eq.iir_eq_db, eq.iir_eq_ph, eq.iir_eq_gd] = eq_compute_response(eq.p_z, ...
eq.p_p, eq.p_k, eq.f, eq.fs);
%% FIR EQ computation

43
tune/eq/eq_compute_response.m
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@ -1,4 +1,4 @@
function [m, ph, gd] = eq_compute_response(b, a, f, fs)
function [m, ph, gd] = eq_compute_response(z, p, k, f, fs)
%%
% Copyright (c) 2016, Intel Corporation
@ -30,16 +30,43 @@ function [m, ph, gd] = eq_compute_response(b, a, f, fs)
% Author: Seppo Ingalsuo <seppo.ingalsuo@linux.intel.com>
%
h = freqz(b, a, f, fs);
m = 20*log10(abs(h));
ph = 180/pi*angle(h);
switch nargin
case 3
b = z; % 1st arg
f = p; % 2nd arg
fs = k; % 3rd arg
h = freqz(b, 1, f, fs);
m = 20*log10(abs(h));
ph = 180/pi*angle(h);
lb = length(b);
la = length(a);
if lb == 1 && la == 1
if length(b) == 1
gd = zeros(1, length(f));
else
else
if exist('OCTAVE_VERSION', 'builtin')
% grpdelay() has some issue so better to not show a plot
gd = NaN * zeros(1, length(f));
else
gd = 1/fs*grpdelay(b, 1, f, fs);
end
end
case 5
[b, a] = zp2tf(z, p, k);
h = freqz(b, a, f, fs);
m = 20*log10(abs(h));
ph = 180/pi*angle(h);
if length(z) == 0 && length(p) == 0
gd = zeros(1, length(f));
else
if exist('OCTAVE_VERSION', 'builtin')
% grpdelay() has some issue so better to not show a plot
gd = NaN * zeros(1, length(f));
else
gd = 1/fs*grpdelay(b, a, f, fs);
end
end
otherwise
error('Incorrect input parameters');
end
end

4
tune/eq/eq_compute_tot_response.m
View File

@ -31,8 +31,8 @@ function eq = eq_compute_tot_response(eq)
%
% FIR response and combined IIR+FIR EQ
[eq.iir_eq_db, eq.iir_eq_ph, eq.iir_eq_gd] = eq_compute_response(eq.b_p, eq.a_p, eq.f, eq.fs);
[eq.fir_eq_db, eq.fir_eq_ph, eq.fir_eq_gd] = eq_compute_response(eq.b_fir, 1, eq.f, eq.fs);
[eq.iir_eq_db, eq.iir_eq_ph, eq.iir_eq_gd] = eq_compute_response(eq.p_z, eq.p_p, eq.p_k, eq.f, eq.fs);
[eq.fir_eq_db, eq.fir_eq_ph, eq.fir_eq_gd] = eq_compute_response(eq.b_fir, eq.f, eq.fs);
eq.tot_eq_db = eq.iir_eq_db + eq.fir_eq_db;
eq.tot_eq_gd = eq.iir_eq_gd + eq.fir_eq_gd;

12
tune/eq/eq_defaults.m
View File

@ -58,7 +58,7 @@ p.fir_autoband = 1;
p.enable_fir = 0;
% IIR conf
p.iir_biquads_max = 6;
p.iir_biquads_max = 8;
p.enable_iir = 0;
% Initialize other fields those are computed later to allow use of struct
@ -73,15 +73,17 @@ p.num_responses = 0;
p.m_db_s = [];
p.gd_s_s = [];
p.logsmooth_noct = 0;
p.b_t = [];
p.a_t = [];
p.t_z = [];
p.t_p = [];
p.t_k = [];
p.t_db = [];
p.m_db_abs = 0;
p.m_db_offs = 0;
p.raw_m_noalign_db = [];
p.err_db = [];
p.b_p = 0;
p.a_p = 0;
p.p_z = [];
p.p_p = [];
p.p_k = [];
p.iir_eq_db = [];
p.iir_eq_ph = [];
p.iir_eq_gd = [];

32
tune/eq/eq_define_parametric_eq.m
View File

@ -1,4 +1,4 @@
function [b_t, a_t] = eq_define_parametric_eq(peq, fs)
function [z, p, k] = eq_define_parametric_eq(peq, fs)
%%
% Copyright (c) 2016, Intel Corporation
@ -36,20 +36,27 @@ PEQ_LS1 = 5; PEQ_LS2 = 6; PEQ_HS1 = 7; PEQ_HS2 = 8;
PEQ_PN2 = 9; PEQ_LP4 = 10; PEQ_HP4 = 11;
sp = size(peq);
b_t = 1; a_t = 1;
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, [b0, a0] = butter(1, 2*f/fs, 'high');
case PEQ_HP2, [b0, a0] = butter(2, 2*f/fs, 'high');
case PEQ_HP4, [b0, a0] = butter(4, 2*f/fs, 'high');
case PEQ_LP1, [b0, a0] = butter(1, 2*f/fs);
case PEQ_LP2, [b0, a0] = butter(2, 2*f/fs);
case PEQ_LP4, [b0, a0] = butter(4, 2*f/fs);
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);
@ -58,7 +65,14 @@ for i=1:sp(1)
otherwise
error('Unknown parametric EQ type');
end
b_t=conv(b_t, b0); a_t = conv(a_t, a0);
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

58
tune/eq/eq_iir_blob_quant.m
View File

@ -1,12 +1,12 @@
function iir_resp = eq_iir_blob_quant(eq_b, eq_a)
function iir_resp = eq_iir_blob_quant(eq_z, eq_p, eq_k)
%% Convert IIR coefficients to 2nd order sections and quantize
%
% iir_resp = eq_iir_blob_quant(b, a, bits)
% iir_resp = eq_iir_blob_quant(z, p, k)
%
% b - numerator coefficients
% a - denominator coefficients
% bits - number of bits to quantize
% z - zeros
% p - poles
% k - gain
%
% iir_resp - vector to setup an IIR equalizer with number of sections, shifts,
% and quantized coefficients
@ -47,21 +47,41 @@ bits_iir = 32; % Q2.30
qf_iir = 30;
bits_gain = 16; % Q2.14
qf_gain = 14;
scale_max = -3; % dB, scale biquad L-inf norm
scale_max = -6; % dB, scale biquads peak gain to this
plot_pz = 0;
plot_fr = 0;
%% Convert IIR to 2nd order sections
if exist('OCTAVE_VERSION', 'builtin')
[sos, gain] = tf2sos(eq_b, eq_a);
else
% TODO: tf2sos produces in Matlab EQs with zero output due to
% very high gain variations within biquad. Need to investigate if
% this is incorrect usage and a bug here.
[sos, gain] = tf2sos(eq_b, eq_a, 'UP', Inf);
fprintf('Warning: Problems have been seen with some IIR designs.\n');
fprintf('Warning: Please check the result.\n');
% This a simple implementation of zp2sos() function. It is not used here due
% to utilization of rather strong scaling and resulting low SNR with the
% available word length in EQ in SOF. This poles and zeros allocation to
% biquads is base only in ascending sort of angular frequency.
sz = length(eq_z);
sp = length(eq_p);
sk = length(eq_k);
nb = max(sz, sp)/2;
az = angle(eq_z);
ap = angle(eq_p);
[~, iz] = sort(abs(az));
[~, ip] = sort(abs(ap));
eq_z = eq_z(iz);
eq_p = eq_p(ip);
sos = zeros(nb, 6);
for i = 1:nb
j = 2*(i-1)+1;
if i == 1
[b, a] = zp2tf(eq_z(j:j+1), eq_p(j:j+1), eq_k);
else
[b, a] = zp2tf(eq_z(j:j+1), eq_p(j:j+1), 1);
end
sos(i,1:3) = b;
sos(i,4:6) = a;
end
gain = 1;
%% Convert 2nd order sections to SOF parameters format and scale the biquads
% with criteria below (Gain max -6 dB at any frequency). Then calculate
% scaling shifts and finally gain multiplier for output.
sz = size(sos);
nbr_sections = sz(1);
n_section_header = 2;
@ -70,10 +90,10 @@ iir_resp = int32(zeros(1,n_section_header+nbr_sections*n_section));
iir_resp(1) = nbr_sections;
iir_resp(2) = nbr_sections; % Note: All sections in series
scale_max_lin = 10^(scale_max/20);
for n=1:nbr_sections
b = sos(n,1:3);
a = sos(n,4:6);
if plot_pz
figure
zplane(b,a);
@ -84,14 +104,12 @@ for n=1:nbr_sections
np = 1024;
[h, w] = freqz(b, a, np);
hm = max(abs(h));
scale = 10^(scale_max/20)/hm;
scale = scale_max_lin/hm;
gain_remain = 1/scale;
gain = gain*gain_remain;
b = b * scale;
ma = max(abs(a));
mb = max(abs(b));
if plot_fr
figure
[h, w] = freqz(b, a, np);
@ -119,6 +137,8 @@ for n=1:nbr_sections
iir_resp(m+5) = section_shift;
iir_resp(m+6) = eq_coef_quant( section_gain, bits_gain, qf_gain);
%fprintf('sec=%d, shift=%d, gain=%f\n', n, section_shift, section_gain);
end
end

4
tune/eq/eq_norm.m
View File

@ -61,13 +61,13 @@ end
%% Adjust FIR and IIR gains if enabled
if eq.enable_fir && eq.enable_iir
eq.b_fir = eq.b_fir * g_fir * g_offs;
eq.b_p = eq.b_p * g_iir * g_offs;
eq.p_k = eq.p_k * g_iir * g_offs;
end
if eq.enable_fir && eq.enable_iir == 0
eq.b_fir = eq.b_fir * g_fir * g_offs;
end
if eq.enable_fir == 0 && eq.enable_iir
eq.b_p = eq.b_p * g_iir * g_offs;
eq.p_k = eq.p_k * g_iir * g_offs;
end
%% Re-compute response after adjusting gain

36
tune/eq/eq_plot.m
View File

@ -115,7 +115,7 @@ if length(eq.b_fir) > 1
end
%% IIR filter
if length(eq.b_p) > 1
if length(eq.p_z) > 1 || length(eq.p_p) > 1
% Response
fh=figure(fn); fn = fn+1;
semilogx(eq.f, eq.iir_eq_db);
@ -128,7 +128,7 @@ if length(eq.b_p) > 1
% Polar
fh=figure(fn); fn = fn+1;
zplane(eq.b_p, eq.a_p);
zplane(eq.p_z, eq.p_p);
grid on;
tstr = sprintf('IIR zeros and poles: %s', eq.name);
title(tstr);
@ -137,7 +137,8 @@ if length(eq.b_p) > 1
ti = 50e-3;
x = zeros(1, ti * round(eq.fs));
x(1) = 1;
y = filter(eq.b_p, eq.a_p, x);
sos = zp2sos(eq.p_z, eq.p_p, eq.p_k);
y = sosfilt(sos, x);
fh=figure(fn); fn = fn+1;
t = (0:(length(x)-1)) / eq.fs;
plot(t, y);
@ -149,28 +150,29 @@ if length(eq.b_p) > 1
end
%% Group delay
fh=figure(fn); fn = fn+1;
if eq.enable_fir && eq.enable_iir
if ~exist('OCTAVE_VERSION', 'builtin')
% Skip plot if running in Octave due to incorrect result
fh=figure(fn); fn = fn+1;
if eq.enable_fir && eq.enable_iir
semilogx(eq.f, eq.tot_eq_gd * 1e3, ...
eq.f, eq.fir_eq_gd * 1e3, '--', ...
eq.f, eq.iir_eq_gd * 1e3, '--');
legend('Combined','FIR','IIR');
end
if eq.enable_fir && eq.enable_iir == 0
end
if eq.enable_fir && eq.enable_iir == 0
semilogx(eq.f, eq.fir_eq_gd * 1e3);
legend('FIR');
end
if eq.enable_fir == 0 && eq.enable_iir
end
if eq.enable_fir == 0 && eq.enable_iir
semilogx(eq.f, eq.iir_eq_gd * 1e3);
legend('IIR');
end
grid on;
xlabel('Frequency (Hz)');
ylabel('Group delay (ms)');
ax = axis; axis([eq.p_fmin eq.p_fmax ax(3:4)]);
tstr = sprintf('Filter group delay: %s', eq.name);
title(tstr);
end
grid on;
xlabel('Frequency (Hz)');
ylabel('Group delay (ms)');
ax = axis; axis([eq.p_fmin eq.p_fmax ax(3:4)]);
tstr = sprintf('Filter group delay: %s', eq.name);
title(tstr);
end

7
tune/eq/example_iir_eq.m
View File

@ -41,12 +41,11 @@ fs = 48e3;
eq_loud = loudness_iir_eq(fs);
%% Define a passthru IIR EQ equalizer
b_pass = [1 0 0];
a_pass = [1 0 0];
[z_pass, p_pass, k_pass] = tf2zp([1 0 0],[1 0 0]);
%% Quantize and pack filter coefficients plus shifts etc.
bq_pass = eq_iir_blob_quant(b_pass, a_pass);
bq_loud = eq_iir_blob_quant(eq_loud.b_p, eq_loud.a_p);
bq_pass = eq_iir_blob_quant(z_pass, p_pass, k_pass);
bq_loud = eq_iir_blob_quant(eq_loud.p_z, eq_loud.p_p, eq_loud.p_k);
%% Build blob
platform_max_channels = 4; % Setup max 4 channels EQ

2
tune/eq/example_spk_eq.m
View File

@ -140,7 +140,7 @@ end
%% Export IIR part
if eq.enable_iir
bq_iir = eq_iir_blob_quant(eq.b_p, eq.a_p);
bq_iir = eq_iir_blob_quant(eq.p_z, eq.p_p, eq.p_k);
bm_iir = eq_iir_blob_merge(platform_max_channels, ...
num_responses, ...
assign_response, ...