dyadup

R2026b

Dyadic upsampling of Laurent polynomial or Laurent matrix

Syntax

Q = dyadup(P)

Description

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

Dyadic Upsampling 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 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

Dyadic Upsampling of Laurent Matrix

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 = $\left[\begin{array}{cc}a\left(z\right)& 2\\ 3& b\left(z\right)\end{array}\right]$.

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

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 — Upsampled Laurent polynomial or Laurent matrix

laurentPolynomial object | laurentMatrix object

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™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The dyadup function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2021b

R2026b: Use thread-based environments

You can use dyadup in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.