IIR Filters: Emulation Accuracy Across Brands

Some IIR filters may produce different results when used in various amplifier/processor brands. Common causes are differences in the way each brand’s software interprets some filter parameters, like Q and bandwidth (BW), and in the conversion between Q & BW. The differences typically appear in parametric (peaking) filters and shelf filters.

The plots below show various implementations of a 10 kHz 10 dB parametric filter. The upper row is for a sampling rate of 48 kHz and the lower for 96 kHz. There is no simple translation between the BW and Q in each implementation, so to help with the comparison, all have been manually & approximately matched by adjusting the BW or Q to give ~ +5dB at 5 kHz. Looking at the both the magnitude and phase, it’s clear that the implementations are different, particularly near the Nyquist frequency of 24kHz for the 48 kHz sampling rate. The 96 kHz implementations are more similar because Nyquist has been pushed out to 48 kHz. However even when overlaid there are subtle differences.

In the plots, the implementations in the right two columns (labelled Linea Research & Powersoft) each have unique equations to create 2nd order analog filters, which are then mapped to 2nd order digital designs using the Bilinear Transform with frequency warping. The plot on the left uses a method proposed by Sophocles Orfanidis which attempts to keep the digital filter shape close to the analog design near the Nyquist frequency. (This method is very similar to the implementation used by Lake Processing). For more details see the 1996 AES Paper “Digital Parametric Equalizer Design with Prescribed Nyquist-Frequency Gain.”

FIR Designer (& FIR Designer M) can be used to emulate IIR filters as part of a complete loudspeaker preset. They both incude multiple branded ‘IIR Filter Mode’ options (including Linea Research & Powersoft) that address these alternative IIR implementations. The Linea Research & Powersoft modes accurately emulate IIR filters for these brands (for loading into System Engineer, and Armonia, respectively). The Generic mode is the default option and offers IIR filters common to all three modes as well as Chebyshev & Elliptic high-pass and low-pass filters and Neville Thiele notched crossovers.

When using FIR Designer to emulate IIR filters for other brands, we recommend trying all modes within the FIR Designer IIR tab, & comparing the plots displayed with the IIR plots generated by your own control software to determine which mode produces the closest match. Note: the Lake FIR 3-way module can accept raw IIR filter coefficients generated by any of the three modes.

For all modes, IIR filter parameters and raw coefficients can be exported to text files, & the parameters copied to the desired control software. This process is automated for some brands (via Direct-To-Processor functionality).

[2022 Update: FIR Designer & FIR Designer M now include One-click IIR conversion between brands, in the IIR Reference Editor]

Useful links

• Orfanidis DSP text book
• Audio EQ Cookbook – Formulae and Equations
• Robert Bristow-Johnson The Equivalent of Various Methods of Computing Biquad Coefficients for Audio Parametric Equalizers