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product detector

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well it looks quite simple. first multiply the incoming signal with a sinusoid of the same carrier frequency. you can do this by using a ring or bridge demodulator. then allow the signal to pass through a filter with frequency response 1/(h(w+wc)+h(w-wc)).h(w) is the frequency response of the filter at the transmitter side. i hope this is what you were looking for, a vsb demodulator.
 
I suppose that you would like some practical advice.

In general, product detectors are nothing more than RF mixers whose RF and LO inputs are the same frequency, and so the output is the modulation translated to 0Hz. Well, thats the general principle, but in practice there are as many different designs of product detectors as there are designs of RF mixers. Now, I tried to find some references on how one specifically designed for VSB might be different than any others and could not find much detail in the books I have. In fact, several references said that most analog televisions demodulate VSB by using an envelope detector for simplicity. A product detector will work fine also and since that is what you are asking, I'm going to make some educated guesses on the details.

In something of this sort, it is essential that the LO be the same frequency as the incoming carrier. So, it would make the most sense to derive the LO from the carrier, in much the same manner as is done with "reduced carrier" or "pilot" SSB. The obvious way to do this is to split off some of the incoming signal, and pass it through a very narrow filter at the carrier frequency, and then apply an amplified version of this to the LO input. Another idea might be to use a PLL to phase-lock an LO oscillator to the incoming signal, but with a low loop bandwidth so to exclude the modulation.

Not knowing what frequencies are involved, I would suggest that the most general purpose and easy to use mixer is a passive ring diode mixer, such as the Mini-Circuits SBL-1 or equivalent. This mixer has IF output frequency range down to DC which is important for VSB since you want to recover the DC content, or nearly DC anyway.

To suggest a PLL or carrier filter requires knowledge of frequencies, which you have not mentioned, so I'm a bit stuck at this point.
 
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