I have not given the issue of transient response a lot of thought, so I'm just going to throw out some ideas. Tell me what you think of them.
The question will be if an ideal speaker system, including a subwoofer, is fed a 100Hz tone that starts at time t=0 and is a cosine wave (so that at t=0, it starts out at max value which means it has an infinitely fast rise time) and it lasts for 1 second and then abruptly stops with an infinitely fast fall time, what should be the response of a perfect subwoofer?
Per Fourier analysis, all signals can be matched by a sum of sine waves. I also assume the subwoofer is fed by a perfect crossover set to pass everything at or below 100Hz and nothing above it. Possibly, this crossover is an active digital crossover. I'm rusty on some of my theory and so if implementing such a perfect filter is not possible, then the filter used will be assumed to be the best that can be realized and will be set so that nothing above 100Hz is passed to the sub even if that means also attenuating some frequencies at or below 100Hz.
This is now fed through a perfect (or near perfect) crossover to a subwoofer.
All the sub has to do therefore is reproduce frequencies at or below 100Hz. Therefore, nothing in the signal being sent to the sub can move fast. In fact, any sharp rise or fall times in the signal will actually be reproduced by the tweeter and/or midrange, not the woofer!
The fastest possible changes the sub must reproduce would be those of a 100Hz sine wave at the maximum amplitude the sub can handle with acceptably low audio distortion. Any frequency/amplitude combination below that changes even slower, so can be ignored.
If a sub can't "track" a 100Hz sine wave it max amplitude, isn't that simply a measure of distortion??? Stated another way, if a woofer can't reproduce some part of a 100Hz signal when the signal stops or starts, it won't be able to properly reproduce any cycles of that signal, not just the ones that start up the signal or stop it. If the start and stop of a signal can't be composed of anything higher than 100Hz, then there is no difference between that part of the signal and the "steady state" part that might be in between the start and stop. Therefore, the woofer will have distortion on all parts of the signal, not just the start and stop of it.
It seems to me there is no such thing as transient response and that what is incorrectly called transient response is really included within the definition of distortion.
Please give me your thoughts about my views on this.
Thanks,
Audioresearch