Roundoff noise of arbitrary linear digital networks

Three matrix expressions are derived for the input, coefficient, and product quantization errors of any one-dimensional arbitrary linear digital network implemented using fixed-point arithmetic. From the product quantization error expression, a matrix expression for the computation of the corresponding roundoff noise variance is presented. These expressions (except the input quantization error) have the flexibility of incorporating the effects of amplitude scaling and structural transformation. Results show that this matrix method of computing roundoff noise variance of any arbitrary fixed-point network is accurate, efficient, and convenient to be used.