# Derive the quantization formula of a sine wave.

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

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