Any DSP nerds around? I've been messing about with concepts related to 1 bit ADCs recently out of s

Any DSP nerds around?

I've been messing about with concepts related to 1 bit ADCs recently out of some curiosity

In playing around, I realised that when we are dealing with 1 bit signals, the and operator and multiplication are orthogonal i.e.

0&0 = 0       0*0 = 0
0&1 = 0       0*1 = 0 
1&0 = 0       1*0 = 0
1&1 = 1       1*1 = 1

Now for a mixer, we want to multiply some signal, by some LO complex signal, and get the output mixed complex signal

So - the question becomes:

If I take a PDM (pulse density modulation) signal and LO, and
&
them together - do I get a mixer.

The answer seems to be yes..

This is a little side tangent from a project where I am trying to make a 1 bit SDR, now I think I need to add as a stretch goal trying to make a digital mixer like this 🤔 In theory, I can take a 1 bit signal into LVDS+ on an FPGA LVDS channel and inject whatever noise or signal on the other signal. To just make PDM, we want to put white noise in there, that works fine. But this tells me maybe there is an opportunity to make a mixer feeding PDM signals in instead of noise.

I wonder if anyone tried something like this or has some thoughts related to it. There is prior art for simply making 1 bit ADC using FPGA channels but I haven't found any literature related to this.

P.S. there are a lot of harmonics - they are mostly from the 1bit conversion and can be mitigated to some extent with MORE NOISE, I am ready to find out that even though it can kind of work, it cannot work well enough to ever be useful, but where is there is too much fun finding out the hard way
pdm_mixer.png
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