Efficient implementation of gammatone filters based on warped cosine modulated filter bank

The paper presents an effective implementation of a gammatone filter bank (GFB) based on a warped cosine modulated filter bank (WCMFB) using an all-pass transform. Examples of practical tasks in which a GFB is used are considered, and its main features and disadvantages are analyzed. A description of a uniform cosine-modulated filter bank is given, and the process of synthesis of a WCMFB using all-pass transform is shown. An optimization method for designing a WCMFB prototype filter to approximate the frequency characteristics of GFB has been developed. The method is based on a multiplicative model of the impulse response of the prototype filter using logistic sigmoid functions. The essence of the proposed method is to optimize the prototype filter in order to minimize the RMS error between the frequency response of the GFB and WCMFB for each channel. A software implementation in Python using the PyTorch library has been performed. Experimental studies of the proposed method have been carried out. The experimental results showed that the WCMFB can be used to approximate the frequency characteristics of the GFB, and the resulting frequency response has monotonic declines due to the use of logistic sigmoid functions. The resulting GFB frequency characteristics approximation error dependence on the number of sigmoids used in the prototype filter is analyzed. The analysis of the computational complexity of the WCMFB is performed, and it is shown how the number of addition and multiplication operations depends on the length of the impulse response of the prototype filter and the number of channels of the filter bank. It is concluded that the use of the WCMFB for the implementation of the GFB can significantly reduce the computational costs of implementing gammatone filters compared with direct implementation.