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 x2(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 had been asked this question in an online quiz.
The question is from Applications of FFT Algorithms topic in section DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing