Coefficient sensitivity in recursive digital filters implemented using microprocessors

The sensitivity of the transfer function of a second-order digital filter to the values of its coefficients is evaluated. Two implementations are compared. The delay (z¿1) operator as the basis for the block diagram is compared with the addition operator {z/(z - 1)}. The latter is the form convenient to implement using a microprocessor. It is shown that the addition operator gives superior sensitivities, particularly for large sampling rates. This means that, for a given coefficient wordlength, the density of available transfer functions is greater.