"Sound signature" is more like "audiophile terminology" than "audio science terminology".
With electronics we are concerned with
noise, distortion, and frequency response, and with amplifiers we can include amplifier power, etc.
With electronics, distortion and frequency response are almost always better than human hearing so usually noise is the only thing to be concerned with (background hiss, hum, or whine). If there is no audible noise there is usually NOTHING to be concerned with! And in that case nothing can be "improved", unless you want an
effect like boosted bass or added reverb, etc.
Usually, noise comes from analog amplification, and usually that's hiss (white noise). Power-line hum can come from the amplifier's power supply or from a ground loop.
Audible noise from a DAC is rare but since USB power is often noisy, if you have a USB-
powered DAC, sometimes noise can leak-into the analog-side of the DAC. (Noise from a computer power supply is usually "whine".)
With speakers, other things come into play such as directivity and interaction with room acoustics. But with speakers and headphones, the main thing is
frequency response, which will also be altered by room acoustics. Distortion in speakers is normally much worse that electronics, but not always audible. You can get bad distortion if you try to get too much bass from a small woofer, etc. Speakers don't generate noise unless they rattle, or something like that.
Audiohoolery is worth reading...