A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequency 800 Hz. The output signal has the frequency (a) zero Hz (b) 0.75 kHz (c) 0.5 kHz (d) 0.25 kHz [solved]

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A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequency 800 Hz. The output signal has the frequency

(a) zero Hz (b) 0.75 kHz
(c) 0.5 kHz (d) 0.25 kHz

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Solution

Given \(f_{s} = 1.5 \,kHz, \,f_{m} = 1\, kHz\)

available frequency components \(= nf_{s} \pm f_{m}\)

So, \(1 \,kHz,\, 2.5 \,kHz,\, 0.5\, kHz\).

\(\therefore\) LPF has \(f_{e} = 0.8 \,kHz\).

So only \(0.5\, kHz\) will be at \(o/p\).

Hence, the correct option is (c).