List of Commands

• NormalizeVec(vec): normalize a vector f so that f.U = [||f||,0,..,0].

• D1SymPolyphaseVec(poly,d): return a polyphase vector Pb that is being symmetrized by a matrix U. Pb = Pa.U, where Pa is the polyphase vector a a mask.

• D1SortSymPolyVec(polyVec): regroup same symmetry pattern together.

• D1MatDegBy2(f1,f3,f4,g1,g2): a 4-by-4 paraunitary matrix that reduces a specific vector of Laurent polynomials with symmetry by 2.

• D1SuppReducedBy2(polyVec): a paraunitary matrix that reduces a vector of Laurent polynomials with symmetry by 2.

• D1MatOrthExtVec(symPolyVec): Matrix Extension with Symmetry Algorithm applys to a paraunitary vector of Laurent polynomials with symmetry without considering the coefficient structure of the vector. For a algorithm that consider the coefficient structure of the vector in algebraic number fields, refers to "D1MatOrthExtAlgQ".

• D1SymPolyphaseMat(poly,d): poly is a mask with symmetry satisfying a_{i,j}(z) = \epsilon_{i,j} z^{dc_i-c_j} a_{i,j}(1/z). return a symmetrization matrix U so that it symmetrizes the polyphase Pa of a. I.e., the matrix Pb = Pa.U is a matrix of Laurent polynomials with symmetry.

• D1NormalizeSymType(polyVec): normalize a vector of Laurent polynomials to standard symmetry pattern 1, -1, 1/z, -1/z.

• D1MatOrthExtMat(polyMatrix): Matrix Extension with Symmetry Algorithm applys to a paraunitary submatrix of Laurent polynomials with symmetry without considering the coefficient structure of the submatrix. For a algorithm that consider the coefficient structure of the vector in algebraic number fields, refers to "D1MatOrthExtAlgQ".