If X1(k) and X2(k) are the N-point DFTs of X1(n) and x2(n) respectively, then what is the N-point DFT of x(n)=ax1(n)+bx2(n)?
(a) X1(ak)+X2(bk)
(b) aX1(k)+bX2(k)
(c) e^akX1(k)+e^bkX2(k)
(d) None of the mentioned
I have been asked this question by my college professor while I was bunking the class.
This intriguing question comes from Properties of DFT topic in chapter Discrete Fourier Transform – Properties and Applications of Digital Signal Processing