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A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is
- a)a highly attenuated square wave at 10kHz
- b)nearly zero.
- c)a nearly perfect cosine wave at 30kHz.
- d)a nearly perfect sine wave at 30kHz
Correct answer is option 'C'. Can you explain this answer?
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Answer:
Bandpass Filter:
A bandpass filter allows only a specified range of frequencies to pass through it while attenuating all other frequencies.
Given Parameters:
- Input signal: 10 kHz even-symmetric square wave
- Centre frequency of bandpass filter: 30 kHz
- 3 dB passband of bandpass filter: 6 kHz
Explanation:
1. Frequency Spectrum of the Input Signal:
- The Fourier series of an even-symmetric square wave contains only odd harmonics.
- The 10 kHz even-symmetric square wave has odd harmonics at 30 kHz, 50 kHz, 70 kHz, and so on.
- Therefore, the frequency spectrum of the input signal has a peak at 30 kHz and other odd harmonics.
2. Bandpass Filter Characteristics:
- The bandpass filter has a centre frequency of 30 kHz and a 3 dB passband of 6 kHz.
- This means that the filter allows frequencies in the range of 27 kHz to 33 kHz with maximum amplitude, and attenuates all other frequencies.
3. Output Signal:
- Since the input signal has a peak at 30 kHz, which lies in the passband of the filter, the filter allows this frequency to pass through it.
- The other odd harmonics of the input signal lie outside the passband of the filter and get attenuated.
- Therefore, the output signal is a nearly perfect cosine wave at 30 kHz.
Hence, option 'C' is the correct answer.
Bandpass Filter:
A bandpass filter allows only a specified range of frequencies to pass through it while attenuating all other frequencies.
Given Parameters:
- Input signal: 10 kHz even-symmetric square wave
- Centre frequency of bandpass filter: 30 kHz
- 3 dB passband of bandpass filter: 6 kHz
Explanation:
1. Frequency Spectrum of the Input Signal:
- The Fourier series of an even-symmetric square wave contains only odd harmonics.
- The 10 kHz even-symmetric square wave has odd harmonics at 30 kHz, 50 kHz, 70 kHz, and so on.
- Therefore, the frequency spectrum of the input signal has a peak at 30 kHz and other odd harmonics.
2. Bandpass Filter Characteristics:
- The bandpass filter has a centre frequency of 30 kHz and a 3 dB passband of 6 kHz.
- This means that the filter allows frequencies in the range of 27 kHz to 33 kHz with maximum amplitude, and attenuates all other frequencies.
3. Output Signal:
- Since the input signal has a peak at 30 kHz, which lies in the passband of the filter, the filter allows this frequency to pass through it.
- The other odd harmonics of the input signal lie outside the passband of the filter and get attenuated.
- Therefore, the output signal is a nearly perfect cosine wave at 30 kHz.
Hence, option 'C' is the correct answer.
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A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output isa)a highly attenuated square wave at 10kHzb)nearly zero.c)a nearly perfect cosine wave at 30kHz.d)a nearly perfect sine wave at 30kHzCorrect answer is option 'C'. Can you explain this answer?
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A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output isa)a highly attenuated square wave at 10kHzb)nearly zero.c)a nearly perfect cosine wave at 30kHz.d)a nearly perfect sine wave at 30kHzCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output isa)a highly attenuated square wave at 10kHzb)nearly zero.c)a nearly perfect cosine wave at 30kHz.d)a nearly perfect sine wave at 30kHzCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output isa)a highly attenuated square wave at 10kHzb)nearly zero.c)a nearly perfect cosine wave at 30kHz.d)a nearly perfect sine wave at 30kHzCorrect answer is option 'C'. Can you explain this answer?.
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