Derive the quantization formula of a sine wave.
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Derive the quantization formula based upon the variance of a sinewave and the variance of distortion due to quantization.
This is the signal to distortion (SDR) ratio for a quantized sinewave. A is the amplitude of the quantized sinewave and Delta is the quantization interval of the analog to digital converter, and the quantization performed is rounding.
Using the variance of a random variable based upon statistical samples. The ratio of these two variances is the signal to distortion ratio for the quantized sine wave.
See attached for formula
keywords: steplength
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The average power in the sinewave can be measured by averaging over the period,
P_S = (1/Period) * int_{period} [A sin(2pi*t/Period)]^2 dt = (1/2)A^2 (1)
The average power in the quantization distortion can be measured in the same way:
P_D = (1/StepLength) * int_{StepLength} (Distortion)^2 dt, (2)
where StepLength is the length of the ...
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