Multiple choice

Directions: Carry One Mark Each.

The signal cos(10$\pi$t + $\frac{\pi}{4}$) is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response $\bigg( \frac{sin (\pi t)}{\pi t} \bigg)$cos$\bigg( 40 \pi t - \frac{\pi}{2} \bigg)$. The filter output is

  1. $\frac{15}{2}$cos$\bigg( 40 \pi t - \frac{\pi}{4} \bigg)$
  2. $\frac{15}{2}\bigg( \frac{sin (\pi t)}{\pi t} \bigg)cos\bigg( 10 \pi t + \frac{\pi}{4} \bigg)$
  3. $\frac{15}{2}cos\bigg( 10 \pi t - \frac{\pi}{4} \bigg)$
  4. $\frac{15}{2}\bigg( \frac{sin (\pi t)}{\pi t} \bigg)cos\bigg( 10 \pi t - \frac{\pi}{2} \bigg)$
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