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The signal x (t) = sin (14000πt) , where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows :
What is the number of sinusoids in the output and their frequencies in kHz?
  • a)
    Number = 1, frequency = 7
  • b)
    Number = 3, frequencies= 2,7,11
  • c)
    Number = 2, frequencies = 2, 7
  • d)
    Number = 2, frequencies = 2, 11
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The signal x (t) = sin (14000πt) , where t is in seconds is sampl...
Given input signal x (t) = sin (1400πt)
Input signal spectrum

Sampled signal spectrum is the spectrum of X(f) which repeats with integer multiples of 9 kHz.
Sampled signal spectrum:

The sampled signal spectrum is passed through a LPF of cutoff frequency 12 KHz. Thus the filtered out sinusoids are of 2 KHz 7 KHz and 11 KHz frequency.
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The signal x (t) = sin (14000πt) , where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows :What is the number of sinusoids in the output and their frequencies in kHz?a)Number = 1, frequency = 7b)Number = 3, frequencies= 2,7,11c)Number = 2, frequencies = 2, 7d)Number = 2, frequencies = 2, 11Correct answer is option 'B'. Can you explain this answer?
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