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Assume a 2-bit midrise quantizer with (voltage,codeword) pairs (-3,0),(-1,1),(1,2),(3,3) where step size delta is clearly 2V. Now, calculating PSQNR using the intervals, we have 20log_10(V_peak/qnoise_peak) so Vmax = 3V or 1.5delta. Of course quantization peak error is delta/2 so I should have 1.5delta/(delta/2)=3 in the log.

Here's the problem: textbooks and almost every tutorial I saw take 2^qbits=2^2=4 inside the log function. I feel like the number of levels(4) gets confused with the number of intervals(3). I'm pretty sure I'm the mistaken one, can you explain me how?

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Peak signal to quantisation noise ratio (I think that's what you mean by PSQNR?) is a rather unusual thing to calculate for signal converters. If you are truly interested in the peak signal and noise, then that comes out as 1.5delta for your example, and counting the intervals is relevant.

What we normally do in signal processing (radio, radar, audio, that sort of thing) where the energy of the signal is all important, is to use rms. It's useful to think about the signal potentially going a little beyond the peak converter levels, and so counting the levels is more appropriate.

Of course, when you get to practical word sizes, N being say 4 or more, the difference between \$2^N\$ and \$2^N-1\$ becomes insignificant.

Be very careful you understand which measure, peak or rms, your various text books are using, and why. Also check whether they are just making a large N assumption.

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