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

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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