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A perfect crossover cap shape a FR curve without changing the tone... or that's my take. But the limits of knowledge on the subject are pretty narrow.
So basically a perfect cap would approach a dead short through the pass band (while disallowing DC to pass).
A perfect capacitor would be open at DC and a short at high frequencies. It is not a realizable device, but a mathematical function to model a circuit. A real capacitor has capacitive, resistive and inductive parasitic elements that keep it from being a perfect capacitor. The same is true for resistors and inductors.Since a DSP crossover is a mathematical process, it gets much closer to the original function. There are still mathematical processes in the digital domain that do not let it be a perfect filter, as thing like phase folding occurs. Luckily with DSP crossovers, the folding process is close to the Fs/2 frequency. By having higher sampling frequencies, the folding process is now outside the audio band with sample rates at 192KHz as Fs/2 is now 96KHz. The higher the precision of the math process (more bit length) the lower the artifacts (or noise floor) becomes.Also with passive components and their value tolerances, matching of parts from channel to channel effects imaging and frequency response variation. This becomes critical in higher order filters to make them work correctly.With new DSP's on the market using 64bit floating point math, the errors are vanishingly small with correct filter topologies. I gave up on passive filters long ago with new generation DSP processors and better DAC's for crossovers.
Note that neither of the images in post no#2 have anything to do with capacitors (per se).
Well duh it's reply not post.a perfect cap's response is one thing but it doen's look anything like either of those images.