In this paper, we examine the sensitivity of state-space digital filters to coefficient quantization errors. A cost function using an Lpnorm criteria is used to measure the deviation in frequency response of the filter. The cost function is used to indicate the connection between roundoff noise and filter sensitivity to coefficient quantization errors. Then based on this cost function it is shown that low roundoff noise state-space digital filters, filters in balanced coordinates, and filters based on polynomials orthogonal on the unit circle have low sensitivity to coefficient quantization errors. Furthermore, the sensitivity of the filters is shown to depend on the second-order modes thereby exhibiting certain robustness and immunity to filter bandwidth.