If x(n) is a finite duration sequence of length L, then the discrete Fourier transform X(k) of x(n) is given as ____________
(a) \(\sum_{n=0}^{N-1}x(n)e^{-j2πkn/N}\)(L<N)(k=0,1,2…N-1)
(b) \(\sum_{n=0}^{N-1}x(n)e^{j2πkn/N}\)(L<N)(k=0,1,2…N-1)
(c) \(\sum_{n=0}^{N-1}x(n)e^{j2πkn/N}\)(L>N)(k=0,1,2…N-1)
(d) \(\sum_{n=0}^{N-1}x(n)e^{-j2πkn/N}\)(L>N)(k=0,1,2…N-1)
I had been asked this question in final exam.
This is a very interesting question from Frequency Domain Sampling DFT in division Discrete Fourier Transform – Properties and Applications of Digital Signal Processing