function X = hilbert(Xr)%  HILBERT  Discrete-time analytic signal via Hilbert transform.%    X = HILBERT(Xr) computes the so-called discrete-time analytic signal%    X = Xr + i*Xi such that Xi is the Hilbert transform of real vector Xr.%    If the input Xr is complex, then only the real part is used: Xr=real(Xr).%    If Xr is a matrix, then HILBERT operates along the columns of Xr.% %    HILBERT(Xr,N) computes the N-point Hilbert transform.  Xr is padded with %    zeros if it has less than N points, and truncated if it has more.  % %    For a discrete-time analytic signal X, the last half of fft(X) is zero, %    and the first (DC) and center (Nyquist) elements of fft(X) are purely real.% %    Example:%      Xr = [1 2 3 4];%      X = hilbert(Xr)%    produces X=[1+1i 2-1i 3-1i 4+1i] such that Xi=imag(X)=[1 -1 -1 1] is the%    Hilbert transform of Xr, and Xr=real(X)=[1 2 3 4].  Note that the last half%    of fft(X)=[10 -4+4i -2 0] is zero (in this example, the last half is just%    the last element).  Also note that the DC and Nyquist elements of fft(X)%    (10 and -2) are purely real.% %    See also fft, ifft.%%    Overloaded functions or methods (ones with the same name in other directories)%       help fdesign/hilbert.m%%    Reference page in Help browser%       doc hilbert%X = signal(hilbert(Xr.s), Xr.time);