polyphase

Polyphase components of Laurent polynomial

Since R2021b

Syntax

[E,O] = polyphase(P)

Description

[E,O] = polyphase(P) returns the even part E and odd part O of the Laurent polynomial P.

Examples

Polyphase Decomposition of Laurent Polynomial

Create the Laurent polynomial $$b(z)=z^3+3z^2-1+2z^{-1}$$.

b = laurentPolynomial(Coefficients=[1 3 0 -1 0 2],MaxOrder=3);

Use the polyphase function to obtain the even and odd parts of $$b(z)$$. Use the helper function helperPrintLaurent to print the Laurent polynomials in algebraic form.

[evenP,oddP] = polyphase(b);
resE = helperPrintLaurent(evenP);
disp(resE)

3*z - 1 + 2*z^(-1)

resO = helperPrintLaurent(oddP);
disp(resO)

z^(2)

Confirm the identity $$E(z^2)+z^{-1}O(z^2)==b(z)$$, where $$E(z)$$ and $$O(z)$$ are the even and odd parts, respectively, of $$b(z)$$.

evenPz2 = dyadup(evenP);
oddPz2 = dyadup(oddP);
lpz = laurentPolynomial(Coefficients=1,MaxOrder=-1);
leftSide = evenPz2+(lpz*oddPz2);
areEqual = (leftSide == b)

areEqual = logical
   1

Input Arguments

P — Laurent polynomial

laurentPolynomial object

Laurent polynomial, specified as a laurentPolynomial object.

Output Arguments

E — Even part

laurentPolynomial object

Even part of the Laurent polynomial P, returned as a laurentPolynomial object. The polynomial E is such that:

E(z²) = [P(z) + P(-z)]/2.

O — Odd part

laurentPolynomial object

Odd part of the Laurent polynomial P, returned as a laurentPolynomial object. The polynomial O is such that:

O(z²) = [P(z) - P(-z)]/ [ 2 z^-1].

Extended Capabilities

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

Version History

Introduced in R2021b