rc2poly

R2026b

Convert reflection coefficients to prediction filter polynomial

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Syntax

a = rc2poly(k)
[a,eFinal] = rc2poly(k,r0)

Description

a = rc2poly(k) returns a vector a of prediction filter coefficients from a vector k of lattice-structure reflection coefficients.

example

[a,eFinal] = rc2poly(k,r0) also returns the final prediction error eFinal, based on the zero-lag autocorrelation r0.

Examples

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Open Live Script

Consider a lattice IIR filter given by a set of reflection coefficients. Find its equivalent prediction filter representation.

k = [0.3090 0.9800 0.0031 0.0082 -0.0082];

a = rc2poly(k)
a = 1×6

    1.0000    0.6148    0.9899    0.0000    0.0032   -0.0082

Input Arguments

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List of reflection coefficients, specified as a vector.

Data Types: single | double
Complex Number Support: Yes

Zero-lag autocorrelation, specified as a scalar.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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Prediction filter coefficients, returned as a row vector of length p+1, where p is the number of elements of k. The function returns the first column of a as 1, thus a(1)=1.

Final prediction error power, returned as a scalar.

Algorithms

Assume a vector of n reflection coefficients, k = [k1 k2 ⋯ kn]. The rc2poly function finds a = [1 a1 a2 ⋯ an] through this recursive relationship:

ai(i)=ki,                   i=1,2,⋯,naj(i)=aj(i−1)+ai(i)ai−j(i−1),  j=1,2,⋯,i−1    ∧    i≥2

Thus, ai = ai(n) is the result of the nth iteration of the recursive relationship. This relationship is based on Levinson’s recursion [1].

References

[1] Kay, Steven M. Modern Spectral Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1988.

Extended Capabilities

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Version History

Introduced before R2006a

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See Also

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