So. First of all, I want to express my gratitude and thanks to Mike - mawyatt. Filter experiments have become a New Year's adventure. You can't buy it in travel agencies!
We are talking about a modest device - a ten-bit counter, small buffers and 7002 transistors. To my surprise, the counter is operational up to 80 MHz. Input resistor - 5kOhm, capacitors - 47nF.
Yes, it's a filter. But NO, it doesn't look like a quartz filter. Moreover, there are two big disadvantages. The center frequency of the filter DOES NOT coincide with the LO frequency. I find it hard to find an explanation.
The second phenomenon is the presence of a parasitic signal at the output when there is no signal at the input. I think there are several reasons: different pulses lengths, different rise and fall speed in individual cells. Some kind of leaks. That is, the capacitors always have some offset, which leads to the generation of LO/10.
I must say that I have read a dozen academic papers on this subject. The shortcomings I found were not mentioned. There are no examples of frequency response. Now everyone has a little understanding of the circuit. Thanks.