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To improve a recently developed mel-cepstrum audio steganalysis method, we present in this paper a method based on Fourier spectrum statistics and mel-cepstrum coefficients, derived from the second-order derivative of the audio signal. Specifically, the statistics of the high-frequency spectrum and the mel-cepstrum coefficients of the second-order derivative are extracted for use in detecting audio steganography. We also design a wavelet-based spectrum and mel-cepstrum audio steganalysis. By applying support vector machines to these features, unadulterated carrier signals (without hidden data) and the steganograms (carrying covert data) are successfully discriminated. Experimental results show that proposed derivative-based and wavelet-based approaches remarkably improve the detection accuracy. Between the two new methods, the derivative-based approach generally delivers a better performance.