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An auditory-based transform is presented in this paper. Through an analysis process, the transform coverts time-domain signals into a set of filter bank output. The frequency responses and distributions of the filter bank are similar to those in the basilar membrane of the cochlea. Signal processing can be conducted in the decomposed signal domain. Through a synthesis process, the decomposed signals can be synthesized back to the original signal through a simple computation. Also, fast algorithms for discrete-time signals are presented for both the forward and inverse transforms. The transform has been approved in theory and validated in experiments. An example on noise reduction application is presented. The proposed transform is robust to background and computational noises and is free from pitch harmonics. The derived fast algorithm can also be used to compute continuous wavelet transform.