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In this paper, we investigate the noise robustness of Wang and Shamma's early auditory (EA) model for the calculation of an auditory spectrum in audio classification applications. First, a stochastic analysis is conducted wherein an approximate expression of the auditory spectrum is derived to justify the noise-suppression property of the EA model. Second, we present an efficient fast Fourier transform (FFT)-based implementation for the calculation of a noise-robust auditory spectrum, which allows flexibility in the extraction of audio features. To evaluate the performance of the proposed FFT-based auditory spectrum, a set of speech/music/noise classification tasks is carried out wherein a support vector machine (SVM) algorithm and a decision tree learning algorithm (C4.5) are used as the classifiers. Features used for classification include conventional Mel-frequency cepstral coefficients (MFCCs), MFCC-like features obtained from the original auditory spectrum (i.e., based on the EA model) and the proposed FFT-based auditory spectrum, as well as spectral features (spectral centroid, bandwidth, etc.) computed from the latter. Compared to the conventional MFCC features, both the MFCC-like and spectral features derived from the proposed FFT-based auditory spectrum show more robust performance in noisy test cases. Test results also indicate that, using the new MFCC-like features, the performance of the proposed FFT-based auditory spectrum is slightly better than that of the original auditory spectrum, while its computational complexity is reduced by an order of magnitude.