Translations:Nonminimum-delay wavelet/16/en

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We see that is a polynomial of degree 2N. Because the autocorrelation is symmetric, it follows that if and only if . Thus, Z is a root of this polynomial if and only if is a root. Moreover, because the polynomial has real coefficients, it follows that for every complex root, the corresponding complex-conjugate root must occur. For example, suppose the autocorrelation is (2, 5, 2), where the center point 5 is at time index 0. The Z-transform of the autocorrelation is . The polynomial can be factored as . We see that -2 is a root and that is also a root.