And here are the original samples (little red circles) and the nearly “perfect” reconstructed analog signal (blue):
All of the samples lie exactly on the rails, but the interpolated signal goes past it, more than 14 dB over the rails. This is a ridiculously long windowed-sinc function for the brick-friggin-wall impulse response. 4096 samples. So it was looking at 2048 samples into the past and 2048 samples into the future to interpolate between any two adjacent samples. Note the interpolated curve always goes through the original samples.