P_SQRT Function

Polynomial spectral factorization.

Usage

result = P_SQRT(c)

Input Parameters

c—An array containing the coefficients of a polynomial.

Returned Value

result—An array of coefficients of the minimum phase spectral factor.

Keywords

None.

Discussion

Given a nonnegative, symmetric polynomial c(z), such that:

c(z) = c(z^–1) > 0

find another polynomial a(z) such that:

c(z) = a(z)a(z^–1)

The array c is in the standard form for ZEROPOLY, which means that the polynomial is:

p = c₀ + c₁z + c₂z² + ... + c_nzⁿ

Note:

Keep the following points in mind when using P_SQRT:

The polynomial returned by P_SQRT is made of positive powers of z. To get a polynomial in z^–1, use the REVERSE function to reverse the coefficient array.

If the polynomial returned from P_SQRT is multiplied by its reverse, such as you can do using the PV-WAVE function REVERSE, the result may be scaled differently than the original array. The returned polynomial may be off by a constant factor.

Example

In this example, P_SQRT is used with the polynomial a(x), such that

x² + 2x + 1 = (x + 1)² = a(x)

Because x² + 2x + 1 = (x + 1)(x + 1), factorizing a(x) should return (x + 1).

a = [1, 2, 1]

PM, P_SQRT(a)

; 1.0000000

; 1.0000000