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A continuous-time signal has frequency content at f = 10 MHz, 50 MHz, and 70 MHz. The signal is sampled at a sampling frequency of 56 MHz and is then passed through a low-pass filter with a cutoff frequency of 15 MHz. The frequency content of the output of the filter will be:
- a)10 MHz
- b)10 MHz and 6 MHz
- c)10 MHz, 6 MHz, and 14MHz
- d)46 MHz
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A continuous-time signal has frequency content at f = 10 MHz, 50 MHz, ...
Calculation:
fs = Sampling Frequency = 56 MHz
The frequencies present at the input are:
fm1 = 10 MHz, fm2 = 50 MHz and, fm3 = 70 MHz
Once sampled, the frequency content at the output will be: fm ± fs
For, fm1 = 10 MHz, the output will contain frequencies of,
= fm1, fm1 ±, fm1 ± 2fs ….
= 10 MHz, 66 MHz, 122 MHz
For, fm2 = 50 MHz, the output will contain frequencies of
= fm2, fm2 ± fs, fm2 ± 2fs ….
= 50 MHz, 6 MHz, 106 MHz, 162 MHz
For, fm3 = 70 MHz, the output will contain frequencies of
= fm3, fm3 ± fs, fm3 ± 2fs ….
= 70 MHz, 14 MHz, 182 MHz ….
When these frequencies are passed through a low pass filter with a cutoff frequency of 15 MHz, the only remaining frequencies at its output will be 6MHz, 10 MHz and 14 MHz.
fs = Sampling Frequency = 56 MHz
The frequencies present at the input are:
fm1 = 10 MHz, fm2 = 50 MHz and, fm3 = 70 MHz
Once sampled, the frequency content at the output will be: fm ± fs
For, fm1 = 10 MHz, the output will contain frequencies of,
= fm1, fm1 ±, fm1 ± 2fs ….
= 10 MHz, 66 MHz, 122 MHz
For, fm2 = 50 MHz, the output will contain frequencies of
= fm2, fm2 ± fs, fm2 ± 2fs ….
= 50 MHz, 6 MHz, 106 MHz, 162 MHz
For, fm3 = 70 MHz, the output will contain frequencies of
= fm3, fm3 ± fs, fm3 ± 2fs ….
= 70 MHz, 14 MHz, 182 MHz ….
When these frequencies are passed through a low pass filter with a cutoff frequency of 15 MHz, the only remaining frequencies at its output will be 6MHz, 10 MHz and 14 MHz.
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A continuous-time signal has frequency content at f = 10 MHz, 50 MHz, and 70 MHz. The signal is sampled at a sampling frequency of 56 MHz and is then passed through a low-pass filter with a cutoff frequency of 15 MHz. The frequency content of the output of the filter will be:a)10 MHzb)10 MHz and 6 MHzc)10 MHz, 6 MHz, and 14MHzd)46 MHzCorrect answer is option 'C'. Can you explain this answer?
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