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What is the value of TN(0) for even degree N?(a) -1(b) +1(c) 0(d) ±1The question was posed to me at a job interview.I want to ask this question from Chebyshev Filters topic in section Digital Filters Design of Digital Signal Processing

Answer»

The CORRECT option is (d) ±1

To explain I would say: We know that a CHEBYSHEV POLYNOMIAL of degree N is defined as

TN(X) = cos(Ncos^-1x), |x|≤1

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

For x=0, we have TN(0)=cos(Ncos^-10)=cos(N.π/2)=±1 for N even.



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