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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