The signal $x(t)=\sin (14000\Pi t)$, where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response $H(f)$ as follows:

$H(f)=\begin{cases} 1, & \left | f \right |\leq 12 kHz .\\ 0,& \left | f \right |> 12 kHz . \end{cases}$

What is the number of sinusoids in the output and their frequencies in kHz?

1. Number = 1, frequency = 7
2. Number = 3, frequencies = 2,7,11
3. Number = 2, frequencies = 2,7
4. Number = 2, frequencies = 7,11

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