Which statement correctly describes the discrete-time representation of a finite-duration, non-periodic signal using the DFT?

• A. The DFT yields a discrete spectrum corresponding to the finite time window.
• B. The DFT requires the signal to be strictly periodic.
• C. The DFT is identical to the CT Fourier transform.
• D. The DFT is unrelated to the time window.

Answer: (A)

The key idea is that the DFT analyzes a finite-length block of data. When you have a finite-duration, non-periodic discrete-time signal, you take that block and compute N frequency samples. This gives a discrete spectrum whose bins correspond to the frequencies that fit within that time window. In other words, the DFT samples the underlying frequency content (the DTFT) at N equally spaced frequencies, so you get a discrete set of spectral values that reflect only the portion of the signal inside the window. The signal itself need not be strictly periodic; the DFT effectively assumes the finite block repeats in time, which is what produces the discrete spectrum. This is different from the continuous-time Fourier transform, which yields a continuous spectrum, and it’s also inherently tied to the finite time window rather than being unrelated to it.