Re: FIR filters
Peter. I agree completely that speaker designers should use all available tools and that the days of passive crossovers with miles of copper, banks of resistors, and nonlinear elements (light bulbs) for protection should be over. To the extent that speaker-level crossovers are used to reduce amplifier channel count, they should be as simple and lossless as possible, their deficiencies compensated for by upstream DSP.
I have a few comments on math and nomenclature. In audio the terms "linearity" and "distortion" are thrown about in ways that dull their meaning. When we talk about linear systems we should mean linear in the conventional sense that the function F(x) is linear if F(Ax + By) = AF(x) + BF
and F(0) = 0. This allows for all manner of frequency or time responses, including non-minimum phase responses where the phase is not uniquely determined by the magnitude, but not for the types of non-linearities where new frequencies are produced, such as harmonic distortion. Traditionally, many linear response anomalies are called distortions (phase distortion, etc.) and sometimes, incorrectly, nonlinear, and this contributes to the confusion.
Further, if we limit ourselves to system models that are time invariant and linear in the above sense, then time and frequency domain representations are equivalent given sufficient detail and duration in each. The "complete" frequency response does indeed tell us everything about the time behavior (the converse is true, too). The smoothed and band-limited magnitude plot in the speaker brochure does not.
As with any subject, it's hard to nail down a logical framework and I don't claim the above ramblings to be complete, just an attempt at increasing the discussion's SNR.
Best,
--Frank
