An Automatic Design Procedure for Low-order IIR Parametric Equalizers
2018
Parametric equalization of an acoustic system aims to compensate for the deviations
of its response from a desired target response using parametric digital filters.
An optimization procedure is presented for the automatic design of a low-order equalizer
using parametric infinite impulse response (IIR) filters, specifically second-order
peaking filters and first-order shelving filters. The proposed procedure minimizes the
sum of square errors (SSE) between the system and the target complex frequency
responses, instead of the commonly used difference in magnitudes, and exploits a
previously unexplored orthogonality property of one particular type of parametric
filter. This brings a series of advantages over the state-of-the-art procedures, such as
an improved mathematical tractability of the equalization problem, with the possibility
of computing analytical expressions for the gradients, an improved initialization
of the parameters, including the global gain of the equalizer, the incorporation of
shelving filters in the optimization procedure, and a more accentuated focus on
the equalization of the more perceptually relevant frequency peaks. Examples of
loudspeaker and room equalization are provided, as well as a note about extending
the procedure to multi-point equalization and transfer function modeling.
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