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HOSIRR.m
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function [lsir, lsir_ndiff, lsir_diff, pars, analysis] = HOSIRR(shir, pars)
% Higher-Order Spatial Impulse Response Rendering (HOSIRR)
% --------------------------------------------------------
% Multi-resolution Higher-order Spatial Impulse Response Rendering
%
% DEPENDENCES
% Spherical-Harmonic-Transform Matlab library
% https://github.com/polarch/Spherical-Harmonic-Transform
% Higher-Order-Ambisonics Matlab library
% https://github.com/polarch/Higher-Order-Ambisonics
%
% INPUT ARGUMENTS
% shir : spherical harmonic domain impulse response
% [signalLength x (order+1)^2]
% pars.chOrdering : {'ACN','WXYZ'} channel ordering convention
% Note: 'WXYZ' refers to "FuMa", which is
% first-order only.
% pars.normScheme : {'N3D','SN3D'}, normalisation convention.
% fully normalised (N3D), or semi-normalised
% (SN3D) conventions are supported.
% pars.fs : sample rate
% pars.ls_dirs_deg : loudspeaker array directions in DEGREES
% [azi elev] convention
% pars.multires_winsize : [winsize_low winsize_2 ... winsize_high]
% pars.multires_xovers : [xover_low ... xover_high]
% pars.RENDER_DIFFUSE : {0,1} 0 off, 1 new diffuse stream via
% ambisonic decoding of diffuseness scaled
% sector signals
% pars.BROADBAND_FIRST_PEAK : {0,1} 0 off, 1 broadband analysis for
% direct
% pars.BROADBAND_DIFFUSENESS : {0,1} 0 diffuseness computed per
% frequency bin, 1 diffuseness computed up
% to "maxDiffFreq_Hz", and replicated for
% all bins
% pars.NORMALIZE_INPUT : Normalize input to max(|insig|) = 1
% pars.maxDiffFreq_Hz : frequency up to which to compute the
% diffuseness parameter for
% pars.alpha_diff : one-pole alpha value for smoothing diff
% y(n) = alpha*y(n-1) + (1-alpha)*x(n)
% pars.decorrelationType : {'phase','noise'}
%
% OUTPUT ARGUMENTS
% lsir : loudspeaker impulse responses
% lsir_ndiff : non-diffuse stream only
% lsir_diff : diffuse stream only
% pars : parameter struct used for the processing
% analysis : {nRes}[nBins x nFrames x nSectors],
% historic DoA estimates (.azim, .elev),
% .energy and diffuseness (.diff) estimates
%
% REFERENCES
% [1] McCormack, L., Pulkki, V., Politis, A., Scheuregger, O. and Marschall,
% M., (2020). "Higher-Order Spatial Impulse Response Rendering:
% Investigating the Perceived Effects of Spherical Order, Dedicated
% Diffuse Rendering, and Frequency Resolution". Journal of the Audio
% Engineering Society, 68(5), pp.338-354.
% [2] McCormack, L., Politis, A., Scheuregger, O., and Pulkki, V. 2019.
% "Higher-order processing of spatial impulse responses". In
% Proceedings of the 23rd International Congress on Acoustics,
% 9--13 September 2019 in Aachen, Germany.
% [3] Politis, A. and Pulkki, V., 2016. "Acoustic intensity, energy-
% density and diffuseness estimation in a directionally-constrained
% region". arXiv preprint arXiv:1609.03409.
% [4] Merimaa, J. and Pulkki, V., 2005. "Spatial impulse response
% rendering I: Analysis and synthesis". Journal of the Audio
% Engineering Society, 53(12), pp.1115-1127.
% [5] Pulkki, V. and Merimaa, J., 2006. "Spatial impulse response
% rendering II: Reproduction of diffuse sound and listening tests".
% Journal of the Audio Engineering Society, 54(1/2), pp.3-20.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Leo McCormack, 22/09/2018
% Archontis Politis, 12/06/2018
% Chris Hold, 17/11/2021
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nSH = size(shir,2);
pars.order = sqrt(nSH)-1;
%%% Defaults/Warnings/Errors:
if ( (pars.order>1) && strcmp(pars.chOrdering, 'WXYZ') )
disp('Warning: WXYZ/FuMa is first-order only. Input signals have been truncated to first-order')
pars.maxOrder = 1;
nSH = int32((pars.maxOrder+1).^2);
shir = shir(:,1:nSH);
end
if (~isfield(pars, 'fs')), error('Please specify "fs"'); end
if (~isfield(pars, 'ls_dirs_deg'))
error('Please specify "ls_dirs_deg", in degrees')
end
if (~isfield(pars, 'multires_winsize')), pars.multires_winsize = 512; end
if (~isfield(pars,'multires_xovers') || isempty(pars.multires_xovers))
nRes = 1;
elseif (length(pars.multires_winsize)~=length(pars.multires_xovers)+1)
error('The number of specified window sizes does not match the number of resolutions')
else
nRes = length(pars.multires_winsize);
end
%%% HO-SIRR
disp('HOSIRR Configuration:'), pars %#ok
% convert to 'ACN/N3D' Ambisonic convention
if strcmp(pars.chOrdering, 'WXYZ')
shir = convert_N3D_Bformat(shir, 'b2n');
elseif (strcmp(pars.chOrdering, 'ACN') && strcmp(pars.normScheme, 'SN3D'))
shir = convert_N3D_SN3D(shir, 'sn2n');
end
lSig = size(shir,1);
if isfield(pars,'NORMALIZE_INPUT') && pars.NORMALIZE_INPUT
% normalise input to max(|insig|) = 1
shir = shir./(max(abs(shir(:,1))));
end
% extract the first highest peak
if pars.BROADBAND_FIRST_PEAK
shir_tmp = shir;
% find the index of highest peak in the omni
[~, peak_ind] = max(abs(shir_tmp(:,1)).^2);
% calculate window
dirwinsize = 64;
direct_win = zeros(lSig,1);
direct_win(peak_ind-dirwinsize/2:peak_ind+dirwinsize/2,1) = hanning(dirwinsize+1);
% extract peak from shir
shir_direct = repmat(direct_win, [1 nSH]).*shir;
shir_tmp = repmat(1-direct_win, [1 nSH]).*shir_tmp;
shir = shir_tmp; % remove peak before running the main loop
clear shir_tmp
end
%%% Intialisations
% zero pad the signal's start and end for STFT
maxWinsize = max(pars.multires_winsize);
if maxWinsize == 1
shir_pad = shir;
else
shir_pad = [zeros(maxWinsize/2, nSH); shir; zeros(maxWinsize*2, nSH)];
end
% Loudspeaker locations and VBAP gain table
ls_dirs_deg = pars.ls_dirs_deg;
nLS = size(ls_dirs_deg,1);
vbap_gtable_res = [2 2]; % azi, elev, step sizes in degrees
gtable = getGainTable(ls_dirs_deg, vbap_gtable_res);
% Sector design
if (~isfield(pars, 'pattern')), pars.pattern = 'pwd'; end
if (~isfield(pars, 'ENABLE_DIFF_PR')), pars.ENABLE_DIFF_PR = true; end
[~,sec_dirs_rad] = getTdesign(2*(pars.order));
A_xyz = computeVelCoeffsMtx(pars.order-1);
[pars.sectorCoeffs, pars.secNorms, sec_dirs_rad] = ...
computeSectorCoeffs(pars.order-1, A_xyz, pars.pattern, [], sec_dirs_rad);
% amplitude normalisation term
beta_A = pars.secNorms(1);
% energy normalisation term
beta_E = pars.secNorms(2);
% Perfect Reconstruction of diffuse component
if pars.ENABLE_DIFF_PR
switch pars.pattern
case 'cardioid'
b_n_an = beamWeightsCardioid2Spherical(pars.order-1);
case 'maxRE'
b_n_an = beamWeightsMaxEV(pars.order-1);
case 'pwd'
b_n_an = beamWeightsHypercardioid2Spherical(pars.order-1);
end
c_n = b_n_an ./ sqrt((2*(0:pars.order-1).'+1) / (4*pi));
c_n_res = 1./(c_n./c_n(1));
else
c_n_res = ones(pars.order, 1);
end
if pars.order~=1
pars.sectorDirs = sec_dirs_rad;
end
numSec = size(pars.sectorCoeffs,2)/4;
% divide signal to frequency regions
if (nRes>1)
xover_order = 500;
shir_res = divide2regions(shir_pad, pars.fs, pars.multires_xovers, xover_order);
else
xover_order = 0;
shir_res = shir_pad;
end
clear insig_pad
% time-frequency processing for each frequency region
maxfftsize = 2*maxWinsize;
lsir_res_ndiff = zeros(lSig + 2*maxfftsize + xover_order, nLS, nRes);
lsir_res_diff = zeros(lSig + 2*maxfftsize + xover_order, nLS, nRes);
%%% Multi-resolution processing
for nr = 1:nRes
disp(['Processing frequency region no. ' num2str(nr)]);
winsize = pars.multires_winsize(nr);
fftsize = 2*winsize; % double the window size for FD convolution
hopsize = winsize/2; % half the window size time-resolution
nBins_anl = winsize/2 + 1; % nBins used for analysis
nBins_syn = fftsize/2 + 1; % nBins used for synthesis
centerfreqs_anl = (0:winsize/2)'*pars.fs/winsize;
if pars.BROADBAND_DIFFUSENESS
if nr==nRes
[~,maxDiffFreq_Ind] = min(abs(centerfreqs_anl-min(pars.maxDiffFreq_Hz)));
else
[~,maxDiffFreq_Ind] = min(abs(centerfreqs_anl-min(pars.maxDiffFreq_Hz,pars.multires_xovers(nr))));
end
end
% storage for estimated parameters
analysis.azim{nr} = nan(nBins_anl, ceil(lSig/hopsize), numSec);
analysis.elev{nr} = nan(nBins_anl, ceil(lSig/hopsize), numSec);
analysis.energy{nr} = nan(nBins_anl, ceil(lSig/hopsize), numSec);
analysis.diff{nr} = nan(nBins_anl, ceil(lSig/hopsize), numSec);
% extended energy analysis
analysis.sf_energy{nr} = nan(ceil(lSig/hopsize),1);
analysis.ndiff_energy{nr} = nan(ceil(lSig/hopsize),1);
analysis.diff_energy{nr} = nan(ceil(lSig/hopsize),1);
% transform window (hanning)
x = 0:(winsize-1);
win = sin(x.*(pi/winsize))'.^2;
% diffuse stream rendering intialisations
switch pars.RENDER_DIFFUSE
case 0
% No diffuse stream
case 1
% New SIRR diffuse stream, based on scaling the sector signals
% with diffuseness estimates and then re-encoding them into
% SHs, and then decoding them to the loudspeaker setup
if pars.order==1
D_ls = sqrt(4*pi/nLS).*getRSH(pars.order, ls_dirs_deg).';
else
Y_enc = diag(replicatePerOrder(c_n_res))*...
getRSH(pars.order-1, pars.sectorDirs*180/pi); % encoder
D_ls = sqrt(4*pi/nLS).*getRSH(pars.order-1, ls_dirs_deg).';
end
end
% diffuseness averaging buffers
if ~pars.BROADBAND_DIFFUSENESS
prev_intensity = zeros(nBins_anl,3,numSec);
prev_energy = zeros(nBins_anl,numSec);
else
prev_intensity = zeros(3,numSec);
prev_energy = zeros(numSec,1);
end
% analysed parameters for each sector
azim = zeros(nBins_anl,numSec);
elev = zeros(nBins_anl,numSec);
diffs = zeros(nBins_anl,numSec);
%%% Main processing loop
idx = 1;
framecount = 1;
progress = 1;
nFrames = ceil((lSig + maxWinsize)/hopsize)+1;
while idx + maxWinsize <= lSig + 2*maxWinsize
% Window input and transform to frequency domain
insig_win = win*ones(1,nSH) .* shir_res(idx+(0:winsize-1),:,nr);
inspec_syn = fft(insig_win, fftsize);
inspec_syn = inspec_syn(1:nBins_syn,:); % keep up to nyquist
% Do analysis using only true resolution
inspec_anl = inspec_syn(1:fftsize/winsize:end,:);
%%% SIRR ANALYSIS %%%
outspec_ndiff = 0;
outspec_diff = 0;
W_S = pars.sectorCoeffs;
s_ana = inspec_anl*W_S;
for n=1:numSec
% weighted pressure-velocity signals for this sector
WXYZ_sec = s_ana(:,4*(n-1) + (1:4));
% Compute Intensity vector for each frequency bin
I = real(conj(WXYZ_sec(:,1)*ones(1,3)) .* WXYZ_sec(:,2:4));
[azim(:,n), elev(:,n)] = cart2sph(I(:,1), I(:,2), I(:,3));
if pars.BROADBAND_DIFFUSENESS
% Compute broad-band active-intensity vector
pvCOV = (WXYZ_sec(1:maxDiffFreq_Ind,:)'*WXYZ_sec(1:maxDiffFreq_Ind,:));
I_diff = real(pvCOV(2:4,1));
energy = 0.5 .* real(trace(pvCOV)); % cast back to real
% Estimating and time averaging of boadband diffuseness
diff_intensity = (1-pars.alpha_diff).*I_diff + pars.alpha_diff.*prev_intensity(:,n);
diff_energy = (1-pars.alpha_diff).*energy + pars.alpha_diff.*prev_energy(n);
prev_intensity(:,n) = diff_intensity;
prev_energy(n) = diff_energy;
diffs(:,n) = 1 - sqrt(sum(diff_intensity.^2)) ./ (diff_energy + eps);
else
energy = 0.5 .* sum(abs(WXYZ_sec).^2,2);
% Time averaging of intensity-vector for the diffuseness
% estimate per bin
diff_intensity = (1-pars.alpha_diff).*I + pars.alpha_diff.*prev_intensity(:,:,n);
diff_energy = (1-pars.alpha_diff).*energy + pars.alpha_diff.*prev_energy(:,n);
diffs(:,n) = 1 - sqrt(sum(diff_intensity.^2,2)) ./ (diff_energy + eps);
prev_intensity(:,:,n) = diff_intensity;
prev_energy(:,n) = diff_energy;
%assert(all(diffs(:,n)<=1.001))
%assert(all(diffs(:,n)>=0))
end
% storage for estimated parameters over time
analysis.azim{nr}(:,framecount,n) = azim(:,n);
analysis.elev{nr}(:,framecount,n) = elev(:,n);
assert(energy>=0)
analysis.energy{nr}(:,framecount,n) = energy;
analysis.diff{nr}(:,framecount,n) = diffs(:,n);
end
%%% SIRR SYNTHESIS %%%
if pars.RENDER_DIFFUSE
z_diff = zeros(nBins_syn, numSec);
end
z_00 = zeros(nBins_syn, numSec);
W_S = pars.sectorCoeffs;
for n=1:numSec
% NON-DIFFUSE PART
ndiffs_sqrt = sqrt(1-diffs(:,n));
% Gain factor computation
eleindex = round((elev(:,n)*180/pi+90)/vbap_gtable_res(2));
aziindex = round(mod(azim(:,n)*180/pi+180,360)/vbap_gtable_res(1));
index = aziindex + (eleindex*181) + 1;
gains = gtable(index,:);
% Interpolate the gains in frequency for proper convolution
if pars.RENDER_DIFFUSE
ndiffgains = gains .* (ndiffs_sqrt*ones(1,nLS));
else
ndiffgains = gains;
end
% Interpolate panning filters
ndiffgains = interpolateFilters(permute(ndiffgains, [3 2 1]), fftsize);
ndiffgains = permute(ndiffgains, [3 2 1]);
% generate non-diffuse stream
z_00(:,n) = inspec_syn*W_S(:, 4*(n-1) + 1);
outspec_ndiff = outspec_ndiff + ndiffgains .* (beta_A.*z_00(:,n)*ones(1,nLS));
% DIFFUSE PART
switch pars.RENDER_DIFFUSE
case 0
% No diffuse-fieldendering
case 1
% New SIRR diffuse stream rendering, based on re-encoding the
% sector signals scaled with the diffuseness estimates
diffgains = sqrt(diffs(:,n));
diffgains = interpolateFilters(permute(diffgains, [3 2 1]), fftsize);
diffgains = permute(diffgains, [3 2 1]);
if pars.order == 1
a_diff = repmat(diffgains, [1 nSH]).*inspec_syn; % Check
else
z_diff(:, n) = diffgains .* sqrt(beta_E) .* z_00(:,n);
end
end
end
if pars.RENDER_DIFFUSE
if pars.order > 1
a_diff = z_diff * Y_enc.';
end % encode
outspec_diff = a_diff * D_ls.'; % decode
end
% decorrelation based on randomising the phase
if isequal(pars.decorrelationType, 'phase')
randomPhi = rand(size(outspec_diff))*2*pi-pi;
outspec_diff = abs(outspec_diff) .* exp(1i*randomPhi);
end
analysis.sf_energy{nr}(framecount,1) = mean((4*pi/nSH)*sum(abs(inspec_syn).^2,2));
analysis.ndiff_energy{nr}(framecount,1) = mean(sum(abs(outspec_ndiff).^2,2));
analysis.diff_energy{nr}(framecount,1) = mean(sum(abs(outspec_diff).^2,2));
analysis.total_energy{nr}(framecount,1) = mean(sum(abs(outspec_ndiff+outspec_diff).^2,2));
% overlap-add synthesis
lsir_win_ndiff = real(ifft([outspec_ndiff; conj(outspec_ndiff(end-1:-1:2,:))]));
lsir_res_ndiff(idx+(0:fftsize-1),:,nr) = lsir_res_ndiff(idx+(0:fftsize-1),:,nr) + lsir_win_ndiff;
if pars.RENDER_DIFFUSE ~= 0
lsir_win_diff = real(ifft([outspec_diff; conj(outspec_diff(end-1:-1:2,:))]));
lsir_res_diff(idx+(0:fftsize-1),:,nr) = lsir_res_diff(idx+(0:fftsize-1),:,nr) + lsir_win_diff;
end
% advance sample pointer
idx = idx + hopsize;
framecount = framecount + 1;
if framecount >= floor(nFrames/10*progress)
fprintf('*');
progress=progress+1;
end
end
fprintf('\ndone\n')
% remove delay caused by the filter interpolation of gains and circular shift
tempout = zeros(size(lsir_res_ndiff(:,:,nr)));
tempout(1:end-winsize/2,:) = lsir_res_ndiff(winsize/2+1:end,:,nr);
lsir_res_ndiff(:,:,nr) = tempout;
if pars.RENDER_DIFFUSE
tempout = zeros(size(lsir_res_diff(:,:,nr)));
tempout(1:end-winsize/2,:) = lsir_res_diff(winsize/2+1:end,:,nr);
lsir_res_diff(:,:,nr) = tempout;
end
end
% Sum signals at different frequency regions
lsir_pad_ndiff = sum(lsir_res_ndiff, 3);
% Remove delay caused by processing
delay = maxWinsize/2 + xover_order/2; % remove also delay of band-pass filtering
lsir_ndiff = lsir_pad_ndiff(delay + (1:lSig), :);
if pars.RENDER_DIFFUSE
lsir_pad_diff = sum(lsir_res_diff, 3);
% Remove delay caused by processing
lsir_diff = lsir_pad_diff(delay + (1:lSig), :);
end
% apply convolution decorrelation to diffuse stream if specified
if isequal(pars.decorrelationType, 'noise') && pars.RENDER_DIFFUSE
% we want to apply just enough noise-based reverberation as
% to suitably decorrelate the signals, but not change the captured room
% characteristics too much. T60s of a very, very dry room should suffice for
% this task:
%t60 = [0.07 0.07 0.06 0.04 0.02 0.01];
t60 = [0.2 0.2 0.16 0.12 0.09 0.04];
fc = [125 250 500 1e3 2e3 4e3];
randmat = synthesizeNoiseReverb(nLS, pars.fs, t60, fc, 1);
% Decorrelation
lsir_diff = fftfilt(randmat, lsir_diff);
clear randmat;
end
if pars.BROADBAND_FIRST_PEAK
% re-introduce peak based on broadband analysis
shir_direct_WXYZ = [shir_direct(:,1).';
shir_direct(:,4).'./sqrt(3);
shir_direct(:,2).'./sqrt(3);
shir_direct(:,3).'./sqrt(3);].';
I = real(repmat(conj(shir_direct_WXYZ(:,1)),[1 3]).*shir_direct_WXYZ(:,2:4));
I = sum(I);
[dir_azim, dir_elev] = cart2sph(I(1,1), I(1,2), I(1,3));
% Gain factor computation
eleindex = round((dir_elev*180/pi+90)/vbap_gtable_res(2));
aziindex = round(mod(dir_azim*180/pi+180,360)/vbap_gtable_res(1));
index = aziindex + (eleindex*181) + 1;
dir_gains = gtable(index,:);
lsir_ndiff = lsir_ndiff + dir_gains .* (shir_direct(:,1)*ones(1,nLS));
end
if pars.RENDER_DIFFUSE
lsir = lsir_ndiff+lsir_diff;
else
lsir = lsir_ndiff;
lsir_diff = 0;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M_interp = interpolateFilters(M, fftsize)
% M filter matrix with y = M*x, size NxLxK,
% N output channels, M input channels, K frequency bins
%
% Archontis Politis, 12/06/2018
winsize = 2*(size(M,3)-1);
M_conj = conj(M(:,:,end-1:-1:2));
M_ifft = ifft(cat(3, M, M_conj), [], 3);
M_ifft = M_ifft(:,:, [(winsize/2+1:end) (1:winsize/2)]); % flip
M_interp = fft(M_ifft, fftsize, 3); % interpolate to fftsize
M_interp = M_interp(:,:,1:fftsize/2+1); % keep up to nyquist
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sigregs = divide2regions(sig, fs, xovers, fir_order)
% DIVIDE2REGIONS Bandpass the signal for multi-window analysis
%
% Archontis Politis, 12/06/2018
% number of frequency regions
nRes = length(xovers)+1;
lIn = size(sig,1);
lOut = lIn+fir_order;
nCH = size(sig,2);
sigregs = zeros(lOut, nCH, nRes);
% create first and last lowpass and highpass in the filterbank
filters = zeros(fir_order+1, nRes);
filters(:,1) = fir1(fir_order, xovers(1)/(fs/2), 'low');
filters(:,nRes) = fir1(fir_order, xovers(nRes-1)/(fs/2), 'high');
for i = 2:(nRes-1)
filters(:,i) = fir1(fir_order, [xovers(i-1) xovers(i)]/(fs/2), 'bandpass');
end
for i = 1:nRes
sigregs(:,:,i) = fftfilt(filters(:,i), [sig; zeros(fir_order,nCH)]);
end
% % omit initial delay of filterbank
% sigregs = sigregs(fir_order/2+1:end-fir_order/2,:,:);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function rir_filt = synthesizeNoiseReverb(nCH, fs, t60, fc, FLATTEN)
%NOISEVERB Simulates a quick and dirty exponential decay reverb tail
%
% order: HOA order
% fs: sample rate
% t60: reverberation times in different bands
% fc: center frequencies of reverberation time bands (octave bands)
%
% Archontis Politis, 12/06/2018
if nargin<5, FLATTEN = 0; end
% number of HOA channels
nSH = nCH;
% number of frequency bands
nBands = length(t60);
% decay constants
alpha = 3*log(10)./t60;
% length of RIR
%lFilt = ceil(max(t60)*fs);
t = (0:1/fs:max(t60)-1/fs)';
lFilt = length(t);
% generate envelopes
env = exp(-t*alpha);
% generate RIRs
rir = randn(lFilt, nSH, nBands);
for k = 1:nBands
rir(:, :, k) = rir(:,:,k).*(env(:,k)*ones(1,nSH));
end
% get filterbank IRs for each band
filterOrder = 200;
h_filt = filterbank(fc, filterOrder, fs);
% filter rirs
rir_filt = zeros(lFilt+ceil(filterOrder/2), nSH);
for n = 1:nSH
h_temp = [squeeze(rir(:,n,:)); zeros(ceil(filterOrder/2), nBands)];
rir_filt(:, n) = sum(fftfilt(h_filt, h_temp), 2);
end
if FLATTEN, rir_filt = equalizeMinphase(rir_filt); end
rir_filt = rir_filt(filterOrder/2+1:end,:); % remove delay
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function h_filt = filterbank(fc, filterOrder, fs)
% fc: the center frequencies of the bands
% Nord: order of hte FIR filter
%
% Archontis Politis, 12/06/2018
if length(fc) == 1
h_filt = 1;
elseif length(fc) == 2
h_filt = zeros(filterOrder+1, 2);
% lowpass
f_ll = 2*fc(1)/sqrt(2);
w_ll = f_ll/(fs/2);
h_filt(:, 1) = fir1(filterOrder, w_ll);
% highpass
f_hh = fc(2)/sqrt(2);
w_hh = f_hh/(fs/2);
h_filt(:, 2) = fir1(filterOrder, w_hh, 'high');
else
Nbands = length(fc);
h_filt = zeros(filterOrder+1, Nbands);
% lowpass
f_ll = 2*fc(1)/sqrt(2);
w_ll = f_ll/(fs/2);
h_filt(:, 1) = fir1(filterOrder, w_ll);
% highpass
f_hh = fc(end)/sqrt(2);
w_hh = f_hh/(fs/2);
h_filt(:, end) = fir1(filterOrder, w_hh, 'high');
% bandpass
for k = 2:Nbands-1
fl = fc(k)/sqrt(2);
fh = 2*fc(k)/sqrt(2);
wl = fl/(fs/2);
wh = fh/(fs/2);
w = [wl wh];
h_filt(:, k) = fir1(filterOrder, w, 'bandpass');
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function rir_filt_flat = equalizeMinphase(rir_filt)
%MAKEFLATVERB Makes the decaying noise spectrally flat
%
% Archontis Politis, 12/06/2018
Nrir = size(rir_filt,2);
for n=1:Nrir
% equalise TDI by its minimum phase form to unity magnitude response
tdi_f = fft(rir_filt(:,n));
tdi_min_f = exp(conj(hilbert(log(abs(tdi_f)))));
tdi_eq = real(ifft(tdi_f./tdi_min_f));
rir_filt_flat(:,n) = tdi_eq;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [sectorCoeffs, secNorms, sec_dirs] = computeSectorCoeffs(orderSec, A_xyz, pattern, grid, sec_dirs)
orderVel = orderSec+1;
if orderSec == 0
% for N=0, do 1 sector, basic DirAC
wxyzCoeffs = [ ...
sqrt(4*pi) 0 0 0;
0 0 sqrt(4*pi/3) 0;
0 0 0 sqrt(4*pi/3);
0 sqrt(4*pi/3) 0 0];
% convert to real SH coefficients to use with the real signals
secNorms = [1 1];
sectorCoeffs = wxyzCoeffs;
sec_dirs = []; % or [0, 0], empty more explicit
else
wxyzCoeffs = [];
if nargin<5
switch grid
case 'AP'
[~, sec_dirs] = getTdesign(orderSec+1);
case 'EP'
[~, sec_dirs] = getTdesign(2*orderSec);
otherwise
error("Use 'AP' or 'EP' grid");
end
end
numSec = size(sec_dirs,1);
switch pattern
case 'cardioid'
b_n = beamWeightsCardioid2Spherical(orderSec);
case 'maxRE'
b_n = beamWeightsMaxEV(orderSec);
case {'pwd', 'hypercardioid'}
b_n = beamWeightsHypercardioid2Spherical(orderSec);
otherwise
error("Unknown sector design! " + pattern);
end
c_n = b_n ./ sqrt((2*(0:orderSec).'+1) / (4*pi)); % remove m
w_nm = diag(replicatePerOrder(c_n)) * getRSH(orderSec, [0,0]);
% amplitude preservation factor
beta_A = (sqrt(4*pi)) / (w_nm(1) * numSec);
% energy preservation factor (sqrt when applied to signals)
beta_E = (4*pi) / (w_nm' * w_nm * numSec);
secNorms = [beta_A, beta_E];
for ns = 1:numSec
% rotate the pattern by rotating the coefficients
azi_sec = sec_dirs(ns, 1);
polar_sec = pi/2-sec_dirs(ns, 2); % from elevation to inclination
c_nm = rotateAxisCoeffs(b_n, polar_sec, azi_sec, 'complex'); % CFH: no compensation here
% get the velocity coeffs
x_nm = A_xyz(1:(orderVel+1)^2, 1:(orderSec+1)^2, 1)*c_nm;
y_nm = A_xyz(1:(orderVel+1)^2, 1:(orderSec+1)^2, 2)*c_nm;
z_nm = A_xyz(1:(orderVel+1)^2, 1:(orderSec+1)^2, 3)*c_nm;
% Pad the (lower order) sector coefficients and stack in
% a matrix together with the velocity ones
c_nm = [c_nm; zeros(2*(orderSec+1)+1,1)];
wxyzCoeffs = [wxyzCoeffs c_nm x_nm y_nm z_nm];
end
% convert to real SH coefficients to use with the real signals
sectorCoeffs = real(complex2realCoeffs(wxyzCoeffs));
end
end