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

A. $$\frac{{15}}{2}\cos \left( {40\pi t - \frac{\pi }{4}} \right)$$

B. $$\frac{{15}}{2}\left( {\frac{{\sin \left( {\pi t} \right)}}{{\pi t}}} \right)\cos \left( {10\pi t + \frac{\pi }{4}} \right)$$

C. $$\frac{{15}}{2}\cos \left( {10\pi t - \frac{\pi }{4}} \right)$$

D. $$\frac{{15}}{2}\left( {\frac{{\sin \left( {\pi t} \right)}}{{\pi t}}} \right)\cos \left( {10\pi t - \frac{\pi }{2}} \right)$$

Answer: Option A