You can generate an analytic signal from a real-valued signal, say, from your conventional receivers without an I/Q output, by using a Hilbert filter.
Once you have an analytic signal, frequency conversion becomes a very straightforward process. In the figure, “Re” is the incoming real-valued signal around 10kHz, “Im” is the imaginary part of the obtained analytic signal, and “Sig” is the down converted version of the incoming signal now at 700Hz.
You can also down convert to (almost) DC, but in that case you need to observe both real and imaginary parts to compute the power of the signal unless you control the phase of your BFO.
Under the presence of some sinusoidal and random noise, we do not get a very clean result and need to do some filtering.
