estnoisem.m

voice box tool box for matlab

    nsms=10.^(nsmdb*nv*tinc/10);  % [8 4 2 1.2] in paper
    qeqimax=1/qeqmin;  % maximum value of Qeq inverse (23)
    qeqimin=1/qeqmax; % minumum value of Qeq per frame inverse

    if isempty(yf)      % provide dummy initialization
        ac=1;               % correction factor (9)
        subwc=nv;                   % force a buffer switch on first loop
        ibuf=0;
        p=x;          % smoothed power spectrum
        sn2=p;              % estimated noise power
        pb=p;               % smoothed noisy speech power (20)
        pb2=pb.^2;
        pminu=p;
        actmin=repmat(Inf,1,nrf);   % Running minimum estimate
        actminsub=actmin;           % sub-window minimum estimate
        actbuf=repmat(Inf,nu,nrf);  % buffer to store subwindow minima
        lminflag=zeros(1,nrf);      % flag to remember local minimum
    else

        if ~nrcum       % initialize values for first frame
            p=yf(1,:);          % smoothed power spectrum
            ac=1;               % correction factor (9)
            sn2=p;              % estimated noise power
            pb=p;               % smoothed noisy speech power (20)
            pb2=pb.^2;
            pminu=p;
            actmin=repmat(Inf,1,nrf);   % Running minimum estimate
            actminsub=actmin;           % sub-window minimum estimate
            subwc=nv;                   % force a buffer switch on first loop
            actbuf=repmat(Inf,nu,nrf);  % buffer to store subwindow minima
            ibuf=0;
            lminflag=zeros(1,nrf);      % flag to remember local minimum
        end

        % loop for each frame

        for t=1:nr              % we use t instead of lambda in the paper
            yft=yf(t,:);        % noise speech power spectrum
            acb=(1+(sum(p)./sum(yft)-1).^2).^(-1);  % alpha_c-bar(t)  (9)
            ac=aca*ac+(1-aca)*max(acb,acmax);       % alpha_c(t)  (10)
            ah=amax*ac.*(1+(p./sn2-1).^2).^(-1);    % alpha_hat: smoothing factor per frequency (11)
            snr=sum(p)/sum(sn2);
            ah=max(ah,min(aminh,snr^snrexp));       % lower limit for alpha_hat (12)

            p=ah.*p+(1-ah).*yft;            % smoothed noisy speech power (3)
            b=min(ah.^2,bmax);              % smoothing constant for estimating periodogram variance (22 + 2 lines)
            pb=b.*pb + (1-b).*p;            % smoothed periodogram (20)
            pb2=b.*pb2 + (1-b).*p.^2;     	% smoothed periodogram squared (21)

            qeqi=max(min((pb2-pb.^2)./(2*sn2.^2),qeqimax),qeqimin/(t+nrcum));   % Qeq inverse (23)
            qiav=sum(qeqi)/nrf;             % Average over all frequencies (23+12 lines) (ignore non-duplication of DC and nyquist terms)
            bc=1+av*sqrt(qiav);             % bias correction factor (23+11 lines)
            bmind=1+2*(nd-1)*(1-md)./(qeqi.^(-1)-2*md);      % we use the simplified form (17) instead of (15)
            bminv=1+2*(nv-1)*(1-mv)./(qeqi.^(-1)-2*mv);      % same expression but for sub windows
            kmod=bc*p.*bmind<actmin;        % Frequency mask for new minimum
            if any(kmod)
                actmin(kmod)=bc*p(kmod).*bmind(kmod);
                actminsub(kmod)=bc*p(kmod).*bminv(kmod);
            end
            if subwc>1 && subwc<nv              % middle of buffer - allow a local minimum
                lminflag=lminflag | kmod;    	% potential local minimum frequency bins
                pminu=min(actminsub,pminu);
                sn2=pminu;
            else
                if subwc>=nv                    % end of buffer - do a buffer switch
                    ibuf=1+rem(ibuf,nu);     	% increment actbuf storage pointer
                    actbuf(ibuf,:)=actmin;    	% save sub-window minimum
                    pminu=min(actbuf,[],1);
                    i=find(qiav<qith);
                    nsm=nsms(i(1));          	% noise slope max
                    lmin=lminflag & ~kmod & actminsub<nsm*pminu & actminsub>pminu;
                    if any(lmin)
                        pminu(lmin)=actminsub(lmin);
                        actbuf(:,lmin)=repmat(pminu(lmin),nu,1);
                    end
                    lminflag(:)=0;
                    actmin(:)=Inf;
                    subwc=0;
                end
            end
            subwc=subwc+1;
            x(t,:)=sn2;
            qisq=sqrt(qeqi);
            % empirical formula for standard error based on Fig 15 of [2]
            xs(t,:)=sn2.*sqrt(0.266*(nd+100*qisq).*qisq/(1+0.005*nd+6/nd)./(0.5*qeqi.^(-1)+nd-1));
        end
    end
    if nargout>1    % we need to store the state for next time
        zo.nrcum=nrcum+nr;      % number of frames so far
        zo.p=p;          % smoothed power spectrum
        zo.ac=ac;               % correction factor (9)
        zo.sn2=sn2;              % estimated noise power
        zo.pb=pb;               % smoothed noisy speech power (20)
        zo.pb2=pb2;
        zo.pminu=pminu;
        zo.actmin=actmin;   % Running minimum estimate
        zo.actminsub=actminsub;           % sub-window minimum estimate
        zo.subwc=subwc;                   % force a buffer switch on first loop
        zo.actbuf=actbuf;  % buffer to store subwindow minima
        zo.ibuf=ibuf;
        zo.lminflag=lminflag;      % flag to remember local minimum
        zo.tinc=tinc;     % must be the last one
        zo.qq=qq;
    end
    if ~nargout
        plot((1:nr),10*log10([sum(x,2)/nrf sum(yf,2)/nrf]))
        legend('noise','input');
        ylabel('Power (dB)');
        xlabel(sprintf('Time (%d ms frames)',round(tinc*1000)));
    end
end

function [m,h,d]=mhvals(d)
% Values are taken from Table 5 in [2]
%[2] R. Martin,"Bias compensation methods for minimum statistics noise power
%               spectral density estimation", Signal Processing Vol 86, pp1215-1229, 2006.

% approx: plot(d.^(-0.5),[m 1-d.^(-0.5)],'x-'), plot(d.^0.5,h,'x-')
persistent dmh
if isempty(dmh)
    dmh=[
        1   0       0;
        2   0.26    0.15;
        5   0.48    0.48;
        8   0.58    0.78;
        10  0.61    0.98;
        15  0.668   1.55;
        20  0.705   2;
        30  0.762   2.3;
        40  0.8     2.52;
        60  0.841   3.1;
        80  0.865   3.38;
        120 0.89    4.15;
        140 0.9     4.35;
        160 0.91    4.25;
        180 0.92    3.9;
        220 0.93    4.1;
        260 0.935   4.7;
        300 0.94    5];
end

if nargin>=1
    i=find(d<=dmh(:,1));
    if isempty(i)
        i=size(dmh,1);
        j=i;
    else
        i=i(1);
        j=i-1;
    end
    if d==dmh(i,1)
        m=dmh(i,2);
        h=dmh(i,3);
    else
        qj=sqrt(dmh(i-1,1));    % interpolate using sqrt(d)
        qi=sqrt(dmh(i,1));
        q=sqrt(d);
        h=dmh(i,3)+(q-qi)*(dmh(j,3)-dmh(i,3))/(qj-qi);
        m=dmh(i,2)+(qi*qj/q-qj)*(dmh(j,2)-dmh(i,2))/(qi-qj);
    end
else
    d=dmh(:,1);
    m=dmh(:,2);
    h=dmh(:,3);
end