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

$\dfrac{15}{2}\cos\left(40\pi t – \dfrac{\pi}{4}\right)$

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

$\dfrac{15}{2}\cos\left(10\pi t – \dfrac{\pi}{4}\right)$

$\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t - \dfrac{\pi}{2}\right)$