Question

Which of the following properties of Chebyshev polynomial is false?

(a) The minor lobes have unequal amplitudes

(b) The polynomial Tm(x) is symmetric for m = even

(c) The polynomial Tm(x) crosses the x axis m times between -1 and 1

(d) Minor lobes exists for |x| < 1

I had been asked this question during an interview.

The doubt is from Adaptive Array in chapter Phased, Adaptive and Binomial Arrays of Antennas

Answer 1

Right answer is (a) The minor lobes have unequal amplitudes

Explanation: The minor lobes have equal amplitudes. The polynomial Tm(x) crosses the x axis m times between -1 and 1.

Minor lobes exist for |x| < 1 and major lobes exist for |x| > 1.