You are thinking of all this completely and thoroughly wrong. If I have a recording with nothing, and I do mean nothing, but an impulse, then (in a nutshell) implied is ringing between samples. When the system reconstruct the signal in the analog domain, the analog reconstruction filters interpolate between samples. "Ringing" will happen between the samples due to the bandlimited analog interpolation. For a signal to be a Dirac impulse, it has to have infinite power and infinite bandwidth. SUCH THING. DOES NOT EXIST.