If two cosine signals with different frequencies are summed and transmitted, what feature allows their separation at the receiver using band-pass filters?

If two cosine signals with different frequencies are summed and transmitted, what feature allows their separation at the receiver using band-pass filters?

• A. They cancel each other out due to phase
• B. They yield a single average frequency
• C. They occupy separate, non-overlapping frequency bands
• D. They require nonlinear demodulation to separate

Answer: (C)

The key idea is separating signals by their frequency content. When you sum two cosines with different frequencies, the combined signal has spectral components at those two distinct frequencies. A band-pass filter passes energy only in a particular frequency range and rejects energy outside that range. If the two frequencies are far enough apart that their spectral regions don’t overlap, you can use one band-pass filter centered on the first frequency to extract that component and another centered on the second frequency to extract the other component. In this way, each original cosine is recovered from the received signal by filtering, without needing any nonlinear processing. The other options don’t fit because phase alone doesn’t guarantee cancellation, a single average frequency doesn’t describe two distinct tones, and nonlinear demodulation isn’t required when the components occupy separate frequency bands.

The key idea is separating signals by their frequency content. When you sum two cosines with different frequencies, the combined signal has spectral components at those two distinct frequencies. A band-pass filter passes energy only in a particular frequency range and rejects energy outside that range. If the two frequencies are far enough apart that their spectral regions don’t overlap, you can use one band-pass filter centered on the first frequency to extract that component and another centered on the second frequency to extract the other component. In this way, each original cosine is recovered from the received signal by filtering, without needing any nonlinear processing. The other options don’t fit because phase alone doesn’t guarantee cancellation, a single average frequency doesn’t describe two distinct tones, and nonlinear demodulation isn’t required when the components occupy separate frequency bands.