Dear StackExchange gurus,
I would like to pose this question from a practical standpoint rather than a theoretical one, although perhaps some context in the latter might come useful.
Real-life devices (say Digital-to-Analog converters for example) have a roll off in their frequency response due to analog front-ends. To find said response (and their inverse) one can use spectral methods (T(f) = out(f)/in(f)), or time-domain methods that will extract the impulse response (Wiener-Hopf equations, LMS, etc).
Now, in time-domain methods we can chose our solution to have the dominant coefficient at the center tap of the filter, or we can choose it to be the first tap (i.e. single sided and with zero delay). Both of these give similar results in some occasions, but there are times when the single sided inverse does not invert the system as well as the two-sided does.
Can someone give me some insight on why this happens? Which of the two approaches is better for equalization (regardless of implementation complexity)?