If windowing is used, it would not make a big difference, if at all. This is a step on the raw data, essentially before starting with FFT or Görtzel or DFT.
It would not, I already tested this, both Goertzel & FFT react in similar manner for introducing windowing. The main question, is do I need a windowing?
Thinking about it for awhile, I came to concept of "perspective", a view angle. If I put a phase error, as it is written in the first few lines of the original message, 0.01 degree as a starting point, than all other parameters lined up.
1. SNR: 0.01 degree imply -> ~80 dB
2. BW: Next, is the bandwidth. Since, this is a "measuring" device I'm trying to build, not a dummy dtmf detector, BW has to be defined differently compare to common definition Peak/ sqrt(2). BW in this perspective is the main peak width At -80 dB.
3. And this 80 dB SNR, consequently, says that windowing is a Must, and suppression of the side lobes > 80 .
4. "Measuring device" means that it has some dynamic range, so my phase error (0.01) stays below this line even magnitude at the ADC input drops significantly. I do not have PGA at this point, and probably don't want to have, as it would be another "stepped line" cause of errors. So defining dynamic range at least 40 dB, or better 60 , I have 80 + (40-60) = 120 - 140 dB.
5. Based on this value, now I'm sure Goertzel is must be 64-bits. In my SNR example, where sng_grt shows 67 dB, plus 40 -test was done at 40 dBc, Goertzel noise floor is 107 dB (if 32-bits math used ) and it's way too low for 120-140.
6. I'd test Goertzel-64 on arduino DUE see if it faster than fft-32, could be. Could be I'm underestimating it's performance.