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They are the same; the SNR as limited by quantization noise specifically is SQNR. SNR is signal to noise ratio in general without being specific as to the noise source. SNR is equal to SQNR when quantization noise is the dominant noise source.


I hope you do not mind, but I am going to change terminology a little bit. Since you mentioned simulations, suppose you are sampling the Gaussian white noise, at the input to the integrator, at a constant rate of $f_s$ samples per second. The point spacing, $Δt$, is $1/f_s$ seconds. Suppose $N$ independent consecutive samples are collected. Then the $N$ ...


Time align the quantized signal with your input signal and subtract to create an error signal (match the amplitudes such as to minimize the error signal). The SNR can then be determined as the ratio of the standard deviation of the input signal (after amplitude matching) to the standard deviation of the error signal (20Log10 of this ratio to be in dB). The ...


To estimate the Signal to Noise Ratio you can use the normalized correlation coefficient to the reference time-aligned sequence. I detail this approach further at this post here including the relationship between correlation coefficient and SNR. Note that "noise" in this context is any deviation of the received signal from the reference sequence such as ...

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