Re: Expanding on FIR vs IIR
Andrew,
Let me first say that I have no ulterior motives here other than to continue the dialog on this topic, as it is one of general interest to me. The reason I decided to compose a reply is that, in my personal experience, few sophisticated users of FIR processing for loudspeakers are utilizing naive brickwall linear phase crossover filter schemes.
Since the axial components of most loudspeaker transducers are predominately minimum phase, recursive minimum phase filters (e.g. biquads) are the right approach for dealing with the predominance of linear transducer phenomena. If you are careful, the off-axis components can also be fairly well behaved. Of course that still leaves one with the aggregate non-minimum phase behaviors, including the crossover response, with the usual choice of an allpass class filter response target (i.e. Linkwitz Riley)
In a perfect world the pre-ringing components of the naive brickwall would cancel each other in the adjacency of the crossover point, but having this occur even for the on-axis listening case is questionable to my mind. Thus, the FIR that people are now developing aren't classic brickwall filters. One common alternative approach is applying an FIR inverse of the global allpass response before the conventional crossover filters.
Since the deviations in implementations of things like biquads and the bilinear transform between various audio dsp platforms are well documented, the chances continuity of inter-system performance on the variety of lower horsepower DSP platforms is far from assured. This has burned more than one manufacturer over time, e.g. the wide variability in EAW KF850 systems or Vertec before V4 locked presets. To my mind this leaves manufacturers with three alternatives:
- "Locked" dsp hardware (ever more common)
- Specific processors and programs for said processors (the Fulcrum Acoustics approach)
- Processing transfer functions available for the (sophisticated) end user to match (EAW and EV offer these)
Many manufacturers would agree with you on this, but I'd like to suggest a counterpoint, or at least a modification. The implicit assumption in this statement is that "work[ing] correctly" means drivers with the most consistent axial magnitude behavior. I would suggest that this not the most important transducer trait. Once the axial magnitude response of a driver can be rendered an arbitrary blank slate through use of DSP, this opens up flexibility to design transducers with maximum performance along other criteria (e.g. output, linearity, of-axis consistency, thermal performance, etc.)
The folks who design transducers, amplifiers, and DSP algorithms for small devices like cell phones are eating the proverbial lunch of the pro audio industry in terms of sophisticated approaches to dealing with both linear and non-linear driver behavior using open and closed loop techniques. Ever increasing use of DSP in our industry will help us traverse along the trail the small driver designers are blazing currently.
