Question

Which of the following represents the chebyshev recursive formula?

(a) Tm(z) = 2zTm-1(z) – Tm-2(z)

(b) Tm(z) = zTm-1(z) – 2Tm-2(z)

(c) Tm(z) = 2Tm-1(z) – zTm-2(z)

(d) Tm(z) = Tm-1(z) – 2zTm-2(z)

The question was posed to me in an online interview.

This intriguing question originated from Adaptive Array topic in section Phased, Adaptive and Binomial Arrays of Antennas

Answer 1

Correct choice is (a) Tm(z) = 2zTm-1(z) – Tm-2(z)

Best explanation: The Chebyshev polynomial of any order m can be derived from the recursive formula. This is one of the main features of the Chebyshev polynomial. It is given by

Tm(z) = 2zTm-1(z) – Tm-2(z).