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The paper provides a sensitivity analysis to measure the loss in accuracy induced by perturbations affecting acyclic computational flows composed of linear convolutions and nonlinear functions. We do not assume a large number of coefficients or input independence for the convolution module, nor strict requirements on the nonlinear function. The analysis is tailored to digital VLSI implementations where perturbations, associated with data quantization, affect the device inputs, coefficients, internal values, and outputs. The sensitivity analysis can be used to measure the loss in accuracy along the computational chain, to characterize the tolerated perturbations, and to dimension the whole architecture.