Step 1: Differentiate between Coherent and Non-coherent Demodulation.
Non-coherent detection does not require a phase-synchronized local carrier. Examples include using envelope detectors (for ASK) or discriminators (for FSK).
Coherent detection requires a local reference signal that is phase-locked to the received carrier. This provides better noise performance.
Step 2: Analyze the options.
(A) Discriminator detection: This is a non-coherent method for FSK that measures the instantaneous frequency.
(B) Bandpass filter and envelope detectors: This is the classic non-coherent FSK receiver structure.
(C) Matched filter: A matched filter is the optimal linear filter for maximizing SNR, but it is often part of a larger receiver structure. While used in coherent systems, "correlation receiver" is a more complete description of the coherent FSK demodulator.
(D) Correlation receiver (or correlator): This is the canonical structure for a coherent detector. It works by multiplying (correlating) the incoming signal with locally generated, synchronized replicas of the possible transmitted signals (e.g., one for frequency \(f_1\) and one for \(f_2\)) and integrating the result. The path with the larger output determines the detected bit. This is the definition of coherent FSK detection.