function [a,g,e] = lpcfit(x,p,h,w,ov) % [a,g,e] = lpcfit(x,p,h,w,ov) Fit LPC to short-time segments % x is a stretch of signal. Using w point (2*h) windows every % h points (128), fit order p LPC models. Return the successive % all-pole coefficients as rows of a, the per-frame gains in g % and the residual excitation in e. % ov nonzero selects overlap-add of window-length % residuals, otherwise successive hop-sized residuals are concatenated % for independent near-perfect reconstruction with lpcsynth. % (default is 1) % 2001-02-25 dpwe@ee.columbia.edu \$Header: /homes/dpwe/matlab/columbiafns/RCS/lpcfit.m,v 1.1 2004/03/30 20:55:52 dpwe Exp \$ if nargin < 2 p = 12; end if nargin < 3 h = 128; end if nargin < 4 w = 2*h; end if nargin < 5 ov = 1; end if (size(x,2) == 1) x = x'; % Convert X from column to row end npts = length(x); nhops = floor(npts/h); % Pad x with zeros so that we can extract complete w-length windows % from it x = [zeros(1,(w-h)/2),x,zeros(1,(w-h/2))]; a = zeros(nhops, p+1); g = zeros(nhops, 1); if ov == 0 e = zeros(1, npts); else e = zeros(1, (nhops-1)*h+w); end % Pre-emphasis pre = [1 -0.9]; x = filter(pre,1,x); for hop = 1:nhops % Extract segment of signal xx = x((hop - 1)*h + [1:w]); % Apply hanning window wxx = xx .* hanning(w)'; % Form autocorrelation (calculates *way* too many points) rxx = xcorr(wxx); % extract just the points we need (middle p+1 points) rxx = rxx(w+[0:p]); % Setup the normal equations R = toeplitz(rxx(1:p)); % Solve for a (horribly inefficient to use full inv()) an = inv(R)*rxx(2:(p+1))'; % Calculate residual by filtering windowed xx aa = [1 -an']; if ov == 0 rs = filter(aa, 1, xx((w-h)/2 + [1:h])); else rs = filter(aa,1,wxx); end G = sqrt(mean(rs.^2)); % Save filter, gain and residual a(hop,:) = aa; g(hop) = G; if ov == 0 e((hop - 1)*h + [1:h]) = rs'/G; else e((hop - 1)*h + [1:w]) = e((hop - 1)*h + [1:w]) + rs/G; end end % Throw away first (win-hop)/2 pts if in overlap mode % for proper synchronization of resynth if ov ~= 0 e = e((1+((w-h)/2)):end); end