fwt_ym.sci

小波分解源代码

function w = FWT_YM(x,L,deg)
// FWT_YM -- Forward Wavelet Transform (periodized Meyer Wavelet)
//  Usage
//    w = FWT_YM(x,L,deg)
//  Inputs
//    x    1-d signal; length(x) = 2^J
//    L    Coarsest Level of V_0;  L << J
//    deg  degree of polynomial window 2 <= deg <=4
//  Outputs
//    w    1-d wavelet transform of x
//
//  Description
//    The Meyer wavelet is defined in the frequency domain.
//    The algorithm is very different from usual quadrature
//    mirror filter algorithms.  See the Ph. D. Thesis of
//    Eric Kolaczyk. To reconstruct use IWT_YM
//
//  See Also
//    IWT_YM, CoarseMeyerCoeff, DetailMeyerCoeff, FineMeyerCoeff
//
//  Copyright Aldo I Maalouf

        y = x;
        x = ShapeAsRow(x);
	if L < 3,
		'L must be >= 3.  Enter new value of L or hit Ctrl-C to break.'
		L = input("L = ?");
	end
//
	nn = length2(x);
	J = log2(nn);
	fhat = mtlb_fft(x);
//
//  Compute Coefficients at Coarse Level.
//

	w(1:(2^L)) = CoarseMeyerCoeff(fhat,L,nn,deg);

//
//  Loop to Get Detail Coefficients for levels  j=L,...,J-2.
//
	for j = L:(J-2),
	  w((2^j+1):(2^(j+1))) = DetailMeyerCoeff(fhat,j,nn,deg);
	end
//
//  Calculate Fine Level Detail Coefficients (for j=J-1).
//
	w((2^(J-1)+1):(2^J)) = FineMeyerCoeff(fhat,nn,deg);
	
	w = ShapeLike(w,y);

endfunction