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

  1. $\dfrac{15}{2}\cos\left(40\pi t – \dfrac{\pi}{4}\right)$
  2. $\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(10\pi t  + \dfrac{\pi}{4}\right)$
  3. $\dfrac{15}{2}\cos\left(10\pi t – \dfrac{\pi}{4}\right)$
  4. $\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t  - \dfrac{\pi}{2}\right)$
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