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I am confused about how does frequency mixer actually work. As we know, if we mix a 5 Mhz and a 20 Mhz signal together, it generates 15 Mhz and 25 Mhz signal (ignore harmonic wave for simplicity). If we connect the signal to spectrum analyser, we'll see four signals, 5 15 20 and 25 Mhz. But here is the problem, what we put into the spectrum analyzer is 5 Mhz and 20 Mhz combined at time domain, and it can be split back into 5 and 20 Mhz by fourier transform, then how does 15 and 25 Mhz being formed?