dyaddown

Dyadic downsampling of Laurent polynomial or Laurent matrix

Since R2021b

Syntax

Q = dyaddown(P)

Description

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

Note

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

Examples

Dyadic Downsampling of Laurent Polynomial

Create the Laurent polynomial $$a(z)=\sum _{k=-5}^6(-1{)}^{k}k{z}^k$$. 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 downsampling of $$a(z)$$.

ddown = dyaddown(a)

ddown = 
  laurentPolynomial with properties:

    Coefficients: [6 4 2 0 -2 -4]
        MaxOrder: 3

degree(ddown)

ans = 5

Dyadic Downsampling of Laurent Matrix

Create two Laurent polynomials:

• $$a(z)=\sum _{k=0}^5(6-k)z^{6-k}$$

• $$b(z)=\sum _{k=0}^5(k+1)z^{-k}$$

lpA = laurentPolynomial(Coefficients=[6:-1:1],MaxOrder=6);
lpB = laurentPolynomial(Coefficients=[1:6],MaxOrder=0);

Create the Laurent matrix matA = $\left[\begin{array}{cc}\mathit{a}\left(\mathit{z}\right)& 1\\ 2& \mathit{b}\left(\mathit{z}\right)\end{array}\right]$.

matA = laurentMatrix(Elements={lpA,1;2,lpB});

Obtain the dyadic downsampling of matA.

matB = dyaddown(matA);

Inspect the elements of matB.

matB.Elements{1,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: [6 4 2]
        MaxOrder: 3

matB.Elements{1,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: 1
        MaxOrder: 0

matB.Elements{2,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: 2
        MaxOrder: 0

matB.Elements{2,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: [1 3 5]
        MaxOrder: 0

Input Arguments

P — Laurent polynomial or Laurent matrix

laurentPolynomial object | laurentMatrix object

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

Output Arguments

Q — Downsampled Laurent polynomial or Laurent matrix

laurentPolynomial object | laurentMatrix object

Downsampled Laurent polynomial or Laurent matrix, returned as a laurentPolynomial object or a laurentMatrix object. Downsampling a Laurent polynomial $$P(z)={\displaystyle \sum _{k=-\infty }^{\infty }{C}_k}{z}^k$$ by two results in the polynomial $$Q(z)={\displaystyle \sum _{k=-\infty }^{\infty }{C}_{2k}}{z}^k$$.

Extended Capabilities

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

Version History

Introduced in R2021b