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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

1. a highly attenuated square wave at 10 kHz.
2. nearly zero.
3. a nearly perfect cosine wave at 30 kHz.
4. a nearly perfect sine wave at 30 kHz.

Correct answer: a nearly perfect sine wave at 30 kHz.

Solution

The bandpass filter is designed to allow frequencies around its center frequency of 30 kHz to pass through while attenuating frequencies outside its passband. Since the 10 kHz square wave is well below the filter's passband, it is significantly attenuated, and the output primarily consists of the fundamental frequency component at the center frequency, resulting in a nearly perfect sine wave at 30 kHz.

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