Peak and shelving filters are parametric infinite impulse response filters which are used for amplifying or attenuating a certain frequency band. Shelving filters are parametrized by their cut-off frequency and gain, and peak filters by center frequency, bandwidth and gain. Such filters can be cascaded in order to perform audio processing tasks like equalization, spectral shaping and modelling of complex transfer functions. Such a filter cascade allows independent optimization of the mentioned parameters of each filter. For this purpose, a novel approach is proposed for deriving the necessary local gradients with respect to the control parameters and for applying the instantaneous backpropagation algorithm to deduce the gradient flow through a cascaded structure. Additionally, the performance of such a filter cascade adapted with the proposed method, is exhibited for head-related transfer function modelling, as an example application.

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In this project, a digital ladder filter has been investigated and expanded. This structure is a simplified digital analog model of the well known analog Moog ladder filter. The goal of this paper is to derive the differentiation expressions of this filter with respect to its control parameters in order to integrate it in machine learning systems. The derivation of the backpropagation method is described in this work, it can be generalized to a Moog filter or a similar filter having any number of stages. Subsequently, the example of an adaptive Moog filter is provided. Finally, a machine learning application example is shown where the filter is integrated in a deep learning framework.

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