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dyadup

Dyadic upsampling of Laurent polynomial or Laurent matrix

    Description

    example

    Q = dyadup(P) upsamples by two the Laurent polynomial or Laurent matrix specified by P. If P is a Laurent matrix, dyadup upsamples the matrix elements. If P is a Laurent matrix, dyadup upsamples the matrix elements.

    Note

    The laurentPolynomial and laurentMatrix objects have their own versions of dyadup. The input data type determines which version is executed.

    Examples

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    Create the Laurent polynomial a(z)=k=-56(-1)kkzk. Obtain the degree of a(z).

    cfs = (-1).^(-5:6).*(-5:6);
    a = laurentPolynomial(Coefficients=fliplr(cfs),MaxOrder=6)
    a = 
      laurentPolynomial with properties:
    
        Coefficients: [6 -5 4 -3 2 -1 0 1 -2 3 -4 5]
            MaxOrder: 6
    
    
    degree(a)
    ans = 11
    

    Obtain the degree of the dyadic upsampling of a(z).

    dup = dyadup(a)
    dup = 
      laurentPolynomial with properties:
    
        Coefficients: [6 0 -5 0 4 0 -3 0 2 0 -1 0 0 0 1 0 -2 0 3 0 -4 0 5]
            MaxOrder: 12
    
    
    degree(dup)
    ans = 22
    

    Create two Laurent polynomials:

    • a(z)=2+4z-1+6z-2

    • b(z)=z+3+5z-1

    lpA = laurentPolynomial(Coefficients=[2 4 6],MaxOrder=0);
    lpB = laurentPolynomial(Coefficients=[1 3 5],MaxOrder=1);

    Create the Laurent matrix matA = [a(z)23b(z)].

    matA = laurentMatrix(Elements={lpA,2;3,lpB});

    Obtain the dyadic upsampling of matA.

    matB = dyadup(matA);

    Inspect the elements of matB.

    matB.Elements{1,1}
    ans = 
      laurentPolynomial with properties:
    
        Coefficients: [2 0 4 0 6]
            MaxOrder: 0
    
    
    matB.Elements{1,2}
    ans = 
      laurentPolynomial with properties:
    
        Coefficients: 2
            MaxOrder: 0
    
    
    matB.Elements{2,1}
    ans = 
      laurentPolynomial with properties:
    
        Coefficients: 3
            MaxOrder: 0
    
    
    matB.Elements{2,2}
    ans = 
      laurentPolynomial with properties:
    
        Coefficients: [1 0 3 0 5]
            MaxOrder: 2
    
    

    Input Arguments

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    Laurent polynomial or Laurent matrix, specified as a laurentPolynomial object or a laurentMatrix object, respectively.

    Output Arguments

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    Upsampled Laurent polynomial or Laurent matrix, returned as a laurentPolynomial object or a laurentMatrix object . Upsampling a Laurent polynomial P(z) by two results in the polynomial Q(z) = P(z2).

    Extended Capabilities

    C/C++ Code Generation
    Generate C and C++ code using MATLAB® Coder™.

    Version History

    Introduced in R2021b