Question

What is the value of chebyshev polynomial of degree 3?

(a) 3x^3+4x

(b) 3x^3-4x

(c) 4x^3+3x

(d) 4x^3-3x

I have been asked this question during a job interview.

This interesting question is from Chebyshev Filters topic in division Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (d) 4x^3-3x

The best I can explain: We know that a chebyshev polynomial of degree N is defined as

TN(x) = cos(Ncos^-1x), |x|≤1; TN(x) = cosh(Ncosh^-1x), |x|>1

And the recursive formula for the chebyshev polynomial of order N is given as

TN(x)=2xTN-1(x)-TN-2(x)

Thus for a chebyshev filter of order 3, we obtain

T3(x)=2xT2(x)-T1(x)=2x(2x^2-1)-x=4x^3-3x.