Question

If x1(n) and x2(n) are two real valued sequences of length N, and let x(n) be a complex valued sequence defined as x(n)=x1(n)+jx2(n), 0≤n≤N-1, then what is the value of x1(n)?

(a) \(\frac{x(n)-x^* (n)}{2}\)

(b) \(\frac{x(n)+x^* (n)}{2}\)

(c) \(\frac{x(n)-x^* (n)}{2j}\)

(d) \(\frac{x(n)+x^* (n)}{2j}\)

I have been asked this question in a job interview.

The doubt is from Applications of FFT Algorithms topic in chapter DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

Answer 1

Correct answer is (b) \(\frac{x(n)+x^* (n)}{2}\)

Easiest explanation: Given x(n)=x1(n)+jx2(n)

=>x*(n)= x1(n)-jx2(n)

Upon adding the above two equations, we get x1(n)=\(\frac{x(n)+x*(n)}{2}\).