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A signal $m(t)$ with bandwidth $500 \mathrm{~Hz}$ is first multiplied by a signal $g(t)$ where

\[ g(t)=\sum_{\mathrm{R}=-\infty}^{\infty}(-1)^{k} \delta\left(t-0.5 \times 10^{-4} k\right) \]

The resulting signal is then passed through an ideal lowpass filter with bandwidth $1 \; \mathrm{kHz}$. The output of the lowpass filter would be

- $\delta(t)$
- $m(t)$
- $0$
- $m(t) \delta(t)$