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What is the formula for chebyshev polynomial TN(x) in recursive form?(a) 2TN-1(x) – TN-2(x)(b) 2TN-1(x) + TN-2(x)(c) 2xTN-1(x) + TN-2(x)(d) 2xTN-1(x) – TN-2(x)This question was addressed to me in final exam.This intriguing question originated from Chebyshev Filters topic in portion Digital Filters Design of Digital Signal Processing |
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Answer» RIGHT option is (d) 2xTN-1(x) – TN-2(x) To explain: We know that a chebyshev polynomial of degree N is defined as TN(x) = cos(Ncos^-1x), |x|≤1 cosh(Ncosh^-1x), |x|>1 From the above formula, it is possible to GENERATE chebyshev polynomial USING the following recursive formula TN(x)= 2xTN-1(x)-TN-2(x), N ≥ 2. |
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