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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 |
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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). |
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