Topic: Signals and Systems
Signal $x[t]=\frac{\sin(100\pi t)}{\pi t}$ is
- A. Time limited and band limited
- B. Time limited but not band limited
- C. Not time limited but band limited
- D. Neither time limited nor band limited
Answer: C. Not time limited but band limited
Explanation: The given signal is a sinc function in the time domain, which extends from $-\infty$ to $+\infty$, making it not time-limited. Its Fourier transform is a rectangular pulse in the frequency domain, strictly confined between $-\omega_c$ and $+\omega_c$ (where $\omega_c = 100\pi$), meaning it is strictly band-limited.