1.

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

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.


Discussion

No Comment Found

Related InterviewSolutions