In a system where two separate cosine signals of different frequencies are summed and transmitted, the receiver splits the signal into two branches and applies band-pass filters to each branch. What is the primary purpose of these band-pass filters?

In a system where two separate cosine signals of different frequencies are summed and transmitted, the receiver splits the signal into two branches and applies band-pass filters to each branch. What is the primary purpose of these band-pass filters?

• A. To convert the signals back to the time domain.
• B. To equalize the amplitudes of the two signals.
• C. To isolate each original signal by selecting its frequency band.
• D. To decode phase information.

Answer: (C)

The key idea is separating signals by frequency. When you sum two cosines at different frequencies, you end up with a single waveform that contains both spectral components. To recover each one in its own path, you use a band-pass filter centered around each signal’s frequency. The filter passes the frequencies near that signal and attenuates the other one, so each branch ends up with essentially only its original cosine. This setup lets you process or demodulate each channel independently without interference from the other, using the amplitude and phase information contained in that passband. The filters aren’t doing time-domain conversion, nor are they primarily meant to equalize amplitudes or decode phase information—their main job is frequency isolation.

The key idea is separating signals by frequency. When you sum two cosines at different frequencies, you end up with a single waveform that contains both spectral components. To recover each one in its own path, you use a band-pass filter centered around each signal’s frequency. The filter passes the frequencies near that signal and attenuates the other one, so each branch ends up with essentially only its original cosine.

This setup lets you process or demodulate each channel independently without interference from the other, using the amplitude and phase information contained in that passband. The filters aren’t doing time-domain conversion, nor are they primarily meant to equalize amplitudes or decode phase information—their main job is frequency isolation.