Effect of word-length truncation on quantized Gaussian random variables

The effect of dividing a quantized Gaussian random variable by an integer N and truncating the remainder is studied. Applications include word-length truncation in digital signal processing when N is a power of 2. It is shown that for an input standard deviation greater than about N/3, the output bias and excess variance are approximately constant and equal to -(N - 1)/2N and (1 - 1/N²)/12, respectively.