1.

TN(-x)=(-1)^NTN(x).(a) True(b) FalseThis question was addressed to me in class test.My question is from Chebyshev Filters in section Digital Filters Design of Digital Signal Processing

Answer» RIGHT option is (a) True

Best explanation: We know that a chebyshev polynomial of degree N is defined as

TN(x) = COS(Ncos^-1x), |x|≤1

cosh(Ncosh^-1x), |x|>1

=> TN(-x)= cos(Ncos^-1(-x))=cos(N(π-cos^-1x))=cos(Nπ-Ncos^-1x)=(-1)^N cos(Ncos^-1x)=(-1)^NTN(x)

THUS we get, TN(-x)=(-1)^NTN(x).


Discussion

No Comment Found

Related InterviewSolutions