function y = time_shear(x, c)% time_shear -- chirp convolution%%  Usage%    y = time_shear(x, c)%%  Inputs%    x     signal vector, must have an odd length (to have a center point)%    c     chirp rate%%  Outputs%    y     the time sheared signal%% If x has bandwidth B and duration d, then y will have bandwidth B and % duration c*N*d/pi.  One must be careful to avoid aliasing in time.% Copyright (C) -- see DiscreteTFDs/Copyrighterror(nargchk(2, 2, nargin));x = x(:);N = length(x);if (rem(N,2)==0)  error('signal length must be odd')endM = (N-1)/2;interp = ceil(2*abs(c)/(2*pi/N));xx = sinc_interp(x,interp)/interp;n = (-2*M:1/interp:2*M)';z = exp(j*c/2*n.^2);y = lconv(xx, z);center = (length(y)+1)/2;y = y(center-interp*M:interp:center+interp*M);y = y*sqrt(c/2/pi);% bad way -- inaccurate answers for large c%interp = 2;%xx = sinc_interp(x,interp);%n = [-4*M*(2*pi/N)/c:4*M*(2*pi/N)/c]'/2;%z = exp(j*c/2*n.^2);%y = lconv(xx, z);%center = (length(y)+1)/2;%y = y(center-interp*M:interp:center+interp*M);%%% another bad way -- does circular convolutions%center = (N+1)/2;%x = [x(center:end) ; x(1:center-1)];%X = fft(x);%X = [X(center+1:end) ; X(1:center)];%Y = time_shear(X,-c);%Y = [Y(center:end) ; Y(1:center-1)];%y = ifft(Y);%y = [y(center+1:end) ; y(1:center)];