In an SSB/CW receiver, what is the purpose of the product detector?

A product detector is a specific type of demodulator used in SSB (Single Sideband) and CW (Continuous Wave) receivers. Its sole purpose is to recover the original audio (the transmitted modulation) from the incoming radio signal. It achieves this by mathematically multiplying—or finding the 'product' of—the intermediate frequency (IF) signal and a locally generated carrier wave from the Beat Frequency Oscillator (BFO). Because SSB and CW signals are transmitted without a carrier, the product detector uses the BFO to reinsert that missing carrier, allowing the original audio to be cleanly extracted. Rejecting unwanted sidebands is the job of the IF filter, and converting the final electrical signals into actual sound waves is the job of the speaker or headphones, not the product detector.