Question

The phase function of a discrete time signal x(n)=a^n, where a=r.e^jθ is?

(a) tan(nθ)

(b) nθ

(c) tan^-1(nθ)

(d) none of the mentioned

I got this question during an online exam.

The question is from Discrete Time Signals in chapter Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

The correct answer is (b) nθ

Best explanation: Given x(n)=a^n=(r.e^jθ)^n = r^n.e^jnθ

=>x(n)=r^n.(cosnθ+jsinnθ)

Phase function is tan^-1(cosnθ/sinnθ)=tan^-1(tan nθ)=nθ.