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Consider the analog signal x(t) = 3 Cos 100πt. This signal is sampled with a frequency of 75 samples per second and at the reconstruction side an ideal LPF having cut-off frequency is 30Hz is used. Determine the frequency component at the output of filter.
- a)50 Hz
- b)0 Hz
- c)25 Hz
- d)75 Hz
Correct answer is option 'C'. Can you explain this answer?
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Consider the analog signal x(t) = 3Cos 100πt. This signal is sample...
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Consider the analog signal x(t) = 3Cos 100πt. This signal is sample...
Given Information:
Analog signal x(t) = 3Cos 100πt
Sampling frequency = 75 samples per second
Reconstruction side LPF cut-off frequency = 30Hz
Solution:
1. Nyquist Frequency:
The Nyquist frequency is half of the sampling frequency. In this case, the Nyquist frequency is 75/2 = 37.5Hz.
2. Aliasing:
The signal x(t) has a frequency component of 100π, which is greater than the Nyquist frequency. This will lead to aliasing.
3. Aliasing Frequency:
The aliasing frequency is the difference between the signal frequency and the nearest multiple of the sampling frequency. In this case, it is |100π - 75k|, where k is an integer.
By calculating the aliasing frequency for k = 1, we get |100π - 75| = 25Hz.
4. Filter Output:
The ideal LPF with a cut-off frequency of 30Hz will remove the high-frequency component due to aliasing.
Therefore, the frequency component at the output of the filter will be 25Hz, which is less than the Nyquist frequency and within the passband of the LPF.
Therefore, the correct answer is option C) 25 Hz.
Analog signal x(t) = 3Cos 100πt
Sampling frequency = 75 samples per second
Reconstruction side LPF cut-off frequency = 30Hz
Solution:
1. Nyquist Frequency:
The Nyquist frequency is half of the sampling frequency. In this case, the Nyquist frequency is 75/2 = 37.5Hz.
2. Aliasing:
The signal x(t) has a frequency component of 100π, which is greater than the Nyquist frequency. This will lead to aliasing.
3. Aliasing Frequency:
The aliasing frequency is the difference between the signal frequency and the nearest multiple of the sampling frequency. In this case, it is |100π - 75k|, where k is an integer.
By calculating the aliasing frequency for k = 1, we get |100π - 75| = 25Hz.
4. Filter Output:
The ideal LPF with a cut-off frequency of 30Hz will remove the high-frequency component due to aliasing.
Therefore, the frequency component at the output of the filter will be 25Hz, which is less than the Nyquist frequency and within the passband of the LPF.
Therefore, the correct answer is option C) 25 Hz.
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