It is demonstrated by elementary means that the Chebyshev polynomials Tn(z) areoptimal for ellipses in C in a way that extends the classical properties for Tn(x) relative to the real interval [-1, 1].
A new procedure for estimating characteristic functions based on a Chebyshev polynomial expansion for the density of the Cosine is developed. Simulation results confirm the usefulness of the method.
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