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blueinblue

2013.09.14

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>> ver

----------------------------------

MATLAB Version 7.3.0.267 (R2006b)

>> type Hilbert

function x = hilbert(xr,n)

%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.

% Copyright 1988-2004 The MathWorks, Inc.

% $Revision: 1.10.4.2 $ $Date: 2004/12/26 22:16:02 $

% References:

% [1] Alan V. Oppenheim and Ronald W. Schafer, Discrete-Time

% Signal Processing, 2nd ed., Prentice-Hall, Upper Saddle River,

% New Jersey, 1998.

%

% [2] S. Lawrence Marple, Jr., Computing the discrete-time analytic

% signal via FFT, IEEE Transactions on Signal Processing, Vol. 47,

% No. 9, September 1999, pp.2600--2603.

if nargin<2, n=[]; end

if ~isreal(xr)

warning('HILBERT ignores imaginary part of input.')

xr = real(xr);

end

% Work along the first nonsingleton dimension

[xr,nshifts] = shiftdim(xr);

if isempty(n)

n = size(xr,1);

end

x = fft(xr,n,1); % n-point FFT over columns.

h = zeros(n,~isempty(x)); % nx1 for nonempty. 0x0 for empty.

if n > 0 && 2*fix(n/2) == n

% even and nonempty

h([1 n/2+1]) = 1;

h(2:n/2) = 2;

elseif n>0

% odd and nonempty

h(1) = 1;

h(2:(n+1)/2) = 2;

end

x = ifft(x.*h(:,ones(1,size(x,2))));

% Convert back to the original shape.

x = shiftdim(x,-nshifts);

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