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Hi,
In my opinion, the answer to your question is: "it depends"
The calculation of converting bits depth to usable dynamic range is a bit (sorry...) too simple to make a decision for all cases.
If the signal is TPDF dithered, then the simplified calculation is 6.02*NumberOfBits - 3.01 dB. (The 3.01 is to allow for the noise floor caused by the dither.)
However, remember that the dither is wide-band noise, and that the measurement of its level is a wide-band RMS measurement and therefore averaged over time. The signal, however, it probably not wide-band at any given moment. This means that if, for example,
you have a sine tone at -93 dB FS in a 16-bit system, the math says that your sine tone will be at the same level as the noise floor. However, it will still be easily audible, since the noise floor's energy is distributed over a much wider bandwidth.
However, if you don't dither your signal, and you drop the sine tone down to -93 dB FS, it won't be a sine tone any more. It will be a nasty square wave-like thing.
http://www.tonmeister.ca/seeing_dither/ shows some visual analogies that might make this more intuitive.
It is also oversimplifying to say that the dither will be below the threshold of audibility for the same reason (of bandwidth). However, it should be considered whether the dither will be below the noise floor of the playback system itself (i.e. the amplifiers
driving the headphones/loudspeakers)
In addition to this, you have to consider that, in cases where you are using "home-made" stimuli recorded for the experiment, it is possible that the initial recording was not done "properly" (whatever that might mean. For example, if your initial recording
peaked at 20 dB below full scale and, in order to normalise the various stimuli, you then wind up applying 20 dB of gain to that recording, you're also bringing up the dither noise floor of the original recording by 20 dB. This means that, when you compare
the various stimuli, you may be "infecting" the experiment with different noise floors (like listening to some of Glen Gould's recordings that are tape spliced from different recordings on different days - the piano keeps playing the Goldberg Variation, but
the tape hiss abruptly changes throughout the piece)
Of course, using stupidly high sampling rates and insane bit depths are extremes that are very likely unnecessary - however, if you don't know whether you'll have a problem or not by fiddling with the gain of the stimuli, it's a brute-force way of buying
insurance...
Cheers -geoff |