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A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) is
- a)10 Hz
- b)60 Hz
- c)30 Hz
- d)90 Hz
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A sinusoid x(t) of unknown frequency is sampled by an impulse train of...
Explanation:
- The sampling period is T=20ms. Therefore, the sampling frequency is fs=1/T=50 Hz.
- The ideal lowpass filter removes all frequency components above the cutoff frequency of 25 Hz.
- After passing the sample train through the ideal lowpass filter, the resulting signal has a frequency of 20 Hz.
- Let the frequency of the original sinusoid be f.
- According to the sampling theorem, the frequency of the sinusoid should be less than or equal to half the sampling frequency.
- Therefore, f <= fs/2="25" hz.="">
- Since the resulting signal after passing through the lowpass filter has a frequency of 20 Hz, the original sinusoid must have had a frequency of 20 Hz or less.
- Therefore, the frequency of the original sinusoid is 20 Hz or less.
- Hence, the correct answer is option C, 30 Hz.
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Community Answer
A sinusoid x(t) of unknown frequency is sampled by an impulse train of...
Period of sampling train, Ts = 20 ms
If frequency of x(t) is fx, then after sampling the signal, the sampled signal has the frequency,
fs - fx = 50 - fx and fs + fx = 50 + fs
Now, the sampled signal is applied to and ideal low pass filter with cut off frequency.
fc = 25 Hz
Now, the o/p of filter carried a single frequency component of 20 Hz
∴, only (fs−fx) component passes through the filter, ie.
fs - fx < 25
and fs - fx = 20
50 - fx = 20
fx = 50 - 20 = 30 Hz
If frequency of x(t) is fx, then after sampling the signal, the sampled signal has the frequency,
fs - fx = 50 - fx and fs + fx = 50 + fs
Now, the sampled signal is applied to and ideal low pass filter with cut off frequency.
fc = 25 Hz
Now, the o/p of filter carried a single frequency component of 20 Hz
∴, only (fs−fx) component passes through the filter, ie.
fs - fx < 25
and fs - fx = 20
50 - fx = 20
fx = 50 - 20 = 30 Hz
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A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) isa)10 Hzb)60 Hzc)30 Hzd)90 HzCorrect answer is option 'C'. Can you explain this answer?
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