Complementary Linear Phase Crossovers
Conventional loudspeaker crossovers often use phase-matched low-pass and high-pass IIR filters. However, only certain crossover filter types inherently provide the magnitude and phase relationships needed for the two outputs to sum flat. Linkwitz-Riley filters are widely used for this reason, and (less commonly) Neville Thiele notched crossovers.
Many other filter types (like Bessel and Butterworth filters) produce peaks or dips in the summed crossover region when used as conventional low-pass/high-pass pairs, as illustrated in the simplified diagrams below.
How FIR Filters Expand Crossover Options
FIR filters provides additional options for crossovers, due to their greater independent control over magnitude and phase. Consequently, almost any desired crossover low-pass or high-pass response shape can be implemented as a linear-phase FIR filter, and a complementary filter can be created with the same phase behaviour. For example, the low-pass (or high-pass) magnitude response of conventional IIR crossover filters, such as Butterworth or Bessel, can be re-created as a linear-phase FIR filter and paired with a complementary-response high-pass (or low-pass) FIR filter, to form a matched pair.
Where flat-summing crossover filters are desired, this FIR filter design approach delivers flexibility in crossover choices, enabling a much wider range of crossover characteristics to be used in multi-way loudspeaker designs. It also enables the use of crossover shapes with inherent directivity benefits in the acoustic response of the multi-way loudspeaker.
(Ulrich Horbach and Don Keele published on this very topic, showing how specific complementary linear-phase crossover response shapes aid in achieving a flatter off-axis magnitude response in a multi-way speaker design.)
About linear-phase FIR filters
Linear-phase FIR filters — with their symmetric impulse responses — trade increased magnitude and phase control for delay. Filters with more complex responses, especially at lower frequencies, inherently have greater bulk delay. See our FIR Filtering guide for more details.
In some applications, like music playback, this delay is usually not an issue. In other applications, like live sound reinforcement, additional processing delay can cause problems with stage monitoring and make aligning the PA with the stage sound more difficult. Therefore the intended application needs to be factored in when choosing a DSP design approach.
Creating Complementary Crossovers in FIR Designer
FIR Designer and FIR Designer M can create complementary linear-phase crossover pairs based on a wide range of conventional crossover characteristics.
Complementary crossover generation is supported for these low-pass and high-pass filter types:
- Bessel
- Butterworth
- Variable-Q (2nd order)
- Chebyshev Type I
- Chebyshev Type II
- Elliptic
Start by selecting a supported low-pass or high-pass crossover prototype on FIR Designer’s FIR Magnitude Adjust tab, and set the filter’s phase response to linear phase. Enable the complementary crossover checkbox Cmp to generate the opposite high-pass or low-pass response from that filter (rather than selecting and configuring a second crossover independently).
The resulting FIR filter is mathematically complementary, so two instances of the same filter running on different channels, one with Cmp enabled, sum to a flat magnitude response with matched linear phase.
Before & after complementary crossover generation
Check box selection for complementary crossover generation
In addition to complementary crossover generation, flat-summing Linkwitz-Riley filters can also be set to linear-phase on the FIR Magnitude Adjust tab. FIR Designer also offers Keele-Horbach Type 1 and Type 2 low-pass and high-pass responses (which are inherently complementary), as well as a range of linear-phase brick-wall crossover filters for applications that require extremely steep slopes and maximum band separation.
About acoustic summation
A flat summed response from the complementary filter pair does not necessarily mean the loudspeaker drivers will sum flat acoustically. The final crossover response also depends on the measured magnitude, phase and relative timing of the drivers. See the Crossover Filter Design tutorial for a practical example of designing FIR crossovers around measured loudspeaker responses.
Crossover Response Targets
Any of the crossover types mentioned above can be set as part of a target response, and FIR Designer’s workflow then used to design processing that changes a loudspeaker driver’s measured response to match that target. The target response, including the selected crossover low-pass or high-pass response, is set on FIR Designer’s Target tab.
Since the natural response of a loudspeaker driver is rarely flat, the processing required to match the target will account for both the driver’s measured response and the desired crossover response.
In a multi-way design with each channel’s processed response matching its target, the acoustic summation will more closely match the ideal. Also, when using Keele-Horbach responses, the overall loudspeaker directivity will more closely match what is intended.
