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%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 f
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