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

• A. \(\frac{{15}}{2}\cos \left( {40{\rm{\pi t}} - \frac{{\rm{\pi }}}{4}} \right)\)
• B. \(\frac{{15}}{2}\left( {\frac{{\sin \left( {{\rm{\pi t}}} \right)}}{{{\rm{\pi t}}}}} \right)\cos \left( {10{\rm{\pi t}} + \frac{{\rm{\pi }}}{4}} \right)\)
• C. \(\frac{{15}}{2}\cos \left( {10{\rm{\pi t}} - \frac{{\rm{\pi }}}{4}} \right)\)
• D. \(\frac{{15}}{2}\left( {\frac{{\sin \left( {{\rm{\pi t}}} \right)}}{2}} \right)\cos \left( {40{\rm{\pi t}} - \frac{{\rm{\pi }}}{2}} \right)\)