One embodiment of the present invention provides a system that cancels fan noise in a computer system. During operation, the system obtains a fan noise signal using a microphone. Next, the system generates a spectral pattern based on the obtained fan noise signal. The system then uses the spectral pattern to identify a corresponding cancellation spectrum in an anti-spectra library. Next, the system generates a noise-canceling signal using the cancellation spectrum. Note that the amount of computation required to cancel fan noise is reduced because generating the noise-canceling signal using the anti-spectra library requires less computation than generating the noise-canceling signal using dynamic noise-cancellation techniques.