A delayed parallel filter structure with an FIR part having improved numerical properties

In real-world applications high-order IIR filters are often converted to series or parallel second-order sections to decrease the negative effects of coefficient truncation and roundoff noise. While series biquads are more common, the parallel structure is gaining more interest due to the possibility of full code parallelization. In addition, it is relatively simple to design a filter directly in a parallel form, which can be efficiently utilized for logarithmic frequency resolution filtering often required in audio. If the numerator order of the original transfer function is higher than that of the denominator, a parallel FIR part arises in addition to the second-order IIR sections. Unfortunately, in this case the gain of the sections and that of the FIR filter can be significantly higher than that of the final transfer function, which requires the downscaling of the filter coefficients to avoid overload. This leads to a significant loss of useful bitdeph. This paper analyzes problem and suggests delaying the IIR part so that there is no overlap between the responses of the FIR part and the second-order sections.