polyphase
Syntax
Description
Examples
Polyphase Decomposition of Laurent Polynomial
Create the Laurent polynomial .
b = laurentPolynomial(Coefficients=[1 3 0 -1 0 2],MaxOrder=3);
Use the polyphase
function to obtain the even and odd parts of . 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 , where and are the even and odd parts, respectively, of .
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
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