Biological systems are often subject to external noise from signal stimuli and environmental perturbations, as well as noises in the intracellular signal transduction pathway. Can different stochastic fluctuations interact to give rise to new emerging behaviors? How can a system reduce noise effects while still being capable of detecting changes in the input signal? Here, we study analytically and computationally the role of nonlinear feedback systems in controlling external noise with the presence of large internal noise. In addition to noise attenuation, we analyze derivatives of Fano factor to study systems' capability of differentiating signal inputs. We find effects of internal noise and external noise may be separated in one slow positive feedback loop system; in particular, the slow loop can decrease external noise and increase robustness of signaling with respect to fluctuations in rate constants, while maintaining the signal output specific to the input. For two feedback loops, we demonstrate that the influence of external noise mainly depends on how the fast loop responds to fluctuations in the input and the slow loop plays a limited role in determining the signal precision. Furthermore, in a dual loop system of one positive feedback and one negative feedback, a slower positive feedback always leads to better noise attenuation; in contrast, a slower negative feedback may not be more beneficial. Our results reveal interesting stochastic effects for systems containing both extrinsic and intrinsic noises, suggesting novel noise filtering strategies in inherently stochastic systems.