Can I hear "significant" differences in digital cables? Short answer: yes, with certain cables, on certain equipment, in certain configurations, for certain purposes, with certain musical material, after a certain break-in time. You should keep in mind that, unlike its counterpart, the transmitted bandwidth of digital audio signals occurs in the megaherz range, and has more in common with video signals than with lower-bandwidth analog audio range. This means that cable impedance must be more closely matched and that deviations from 75 Ohm (for S/PDIF) and 110 Ohm (for AES/EBU) will seriously deform digital waveforms. If you have no idea what a deformed digital wave sounds like, use a Y-cord to split a digital signal between two recorders and listen to the result.
In addition, the best cable manufacturers design digital cables to avoid another common cause of errors: reflections in the signal path. Along with impedance mismatch, reflections can cause a decrease in rise time, and a misinterpretation of the actual zero-crossing point of the waveform.
The sonic results of passing a digital signal through an inferior digital cable are as follows: 1.) increased "graininess" (the sound is no longer as smooth), 2.) loss of focus and sharp edges in instrument position; 3.) apparent loss of level, making the listener wanting to turn the level up during soft passages, even though high-level signals are reproduced at proper gain; 4.) spurious (phantom) tones; 5.) added noise and distortion; 6.) loss of low-level resolution. These effects should be audible at all listening volumes. Nevertheless, they are subtle, and some say that they require high-quality digital equipment with audiophile musical material to be audible at all. Other audiophiles go so far as to say that the effects are not audible at all with most recorded music today and that expensive digital cables are a waste of money.
Nevertheless, others claim to hear the differences. To satisfy their qualms, cable manufacturers have started to produce better and/or more expensive digital cables. In the process, some manufacturers have discovered that a superior digital cable is just as difficult to design as a superior analog cable. Careful tests, that should accompany the development of a digital cable, are expensive to carry out, and the exact causes of differences in digital cables has not yet been fully uncovered. Besides the points about impedance and reflection that I have already mentioned, there are some theories that the power supplies of digital components carry a small residual of errors to different stages in digital components due to high-frequency energy dissipation giving rise to logic-induced modulation. These errors can be carried by both digital interconnects and power cables hooked up to digital components. But this is a topic for another day...
If you use several digital devices in a daisy-chain fashion (A/D - digital preamp - digital EQ - D/A - Digital recorder, in whatever configuration), the possible side-effects of poor digital cables become more possible. If you do not use a digital distribution system, then you should probably think about testing different digital cables. No reliable listening test of a S/PDIF cable can be conducted over the weekend, because burn-in time is long. Because of their lower peak-to-peak voltage levels, some S/PDIF cables can take over 1,000 hours playing time before they reveal their true nature; AES/EBU takes less time because of a different configuration. Contrary to the advisability of short analog signal paths, short digital interconnects can give rise to more errors than longer ones. A cable length of 1.5 meters is thought to be the minimum recommendable length by some people, with improvements sometimes achievable with even longer runs, as long as these are not too long (over 100 meters).
