MichaelFremer

Thank you, everyone!

No, I'm not the well-known Michael Fremer and I didn't think anyone would read that into a handle. When I posted my first question here a couple of years ago I had fairly recently been at the Rocky Mountain Audio Fest and in one of the rooms had seen this rather pretentious attender grilling the exhibitor about something. I don't remember how, but I eventually learned it was MF. I had never heard of him. When I needed a handle that's just what popped into my head. Anyway, thank you for your answers.

My understanding is that the dB SPL scale describes actual volume levels and the dBFS scale describes relative volumes such that if I have a room with an ambient noise level of 35 dB SPL I can play a 16-bit audio file with a dynamic range of 96 dB and, as long as my amp and speakers have their level set such that the quietest sound from the file, -96 dBFS, is played at 36 dB SPL, then I can hear the entire dynamic range of the file from 36 dB SPL to 132 dB SPL. Leaving aside the fact that those upper volumes are a problem for humans, is that the right understanding of how dynamic range works?

So I guess a human could look at a sample stream and, seeing many very high numbers, realize immediately that the signal is hot and possibly clipped, but without calculating he could not determine more than that. Right?

Wow. Thank you so much for those detailed answers! I stumbled into that problem while I was trying to figure out what the sample stream would look like at 0 dBFS. My intuition first told me it would be 32768,-32768,32768,-32768.... A wave nearing 0 dBFS would be 32767,-32767..., etc. Then with more thinking I realized I had that wrong. There could be many, many different sample streams that equal 0 dBFS. Any set of samples that describes a wave that peaks at 32,768 (or whatever the highest value on the quantizing scale is) would qualify even though none of the samples are 32,768 because none of them happen at the instant the wave peaks. So most of the time no human could just glance at a sample stream and, without calculating, see the wave is at 0 dBFS. This also explains how a clipped wave can be described, even though any individual sample word cannot go beyond the peak value. A wave that extends beyond the peak values can still be accurately described by samples taken during the parts of the wave that are within the scale. Do I have that right?

I guess I'm not understanding how digital sampling works. Each sample is a measurement of the signal's instantaneous amplitude and assigned the closest value from the quantizing scale, right? Nyquist says you have to sample at a minimum of twice the rate of your highest frequency, right? So suppose you have a sign wave at a frequency exactly half the sampling rate, which satisfies the Nyquist requirement. That means each wave cycle is sampled twice. It also means every cycle is sampled at the same two points. For example, if the sampler happens to be sampling as the cycle crosses the the X-axis then every sample will be 0 (or whatever value the quantizing scale assigns to that point). So your PCM stream will be 0,0,0,0... That's enough data to specify the frequency, but how do you get the amplitude out of it? A wave at a given frequency passes through 0 twice every cycle, regardless of the amplitude. How does knowing my wave hits 0 at every sample tell me anything about how high the wave peaks in between?

Mac w/iTunes --> Airport Express --> TOSlink to AudioEngine D1 DAC --> AudioEngine A5 speakers For the best sound is there a rule of thumb for the volume settings? It can be set in iTunes, on the D1 and on the A5s. The iTunes volume must affect the bitstream from the AE in some way. Does that mean quality reduction? Is there a volume at which the bitstream is identical to the source material? For the analog signal is it better to have the volume low on the D1 and high on the A5s, or vice-versa, or 50-50, or does it not matter? Thanks!