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 + ... + cnzn
 
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
See Also
In the PV‑WAVE Reference: REVERSE