In our continuing series on PCM vs. DSD I mentioned a day or so ago that bit depth controlled two things: granularity as well as dynamic range. Granularity being the fineness of each step in voltage when we think of rebuilding the signal back into a continuous waveform and dynamics being the difference between the softest and the loudest sound we can reproduce. I wanted to take a closer look at how these steps in a PCM system looked and put things in perspective. Then we'll move onto to the reconstruction of the waveform from numbers back into voltage and music. Here's what a sine wave made out of discrete steps looks like: Note carefully how the little steps look: each being a discrete sample of a fixed voltage point along the way. There are a couple of things to think about when you see this: the sharp "stairs" we see were never in the original music and what happens in between each of the fixed steps? The sharp steps we see all have edges that are artifacts of the snapshot process and you'll understand their presence better if we use our movie analysis. Think of those each step as a single frame in the move example - when you run the movie they go fast enough you don't notice the steps (or frames) but they are, in fact, there and later I'll explain to you how we "eliminate" them. If each of the discrete fixed samples is the only record we have of the original moving signal, what happens if the voltage changed between the time we took a sample and the next sample? If something did happen we'd totally miss it. This is controlled by the sample rate which determines the maximum high frequency content. 44.1kHz gives us a maximum rate of change of half that value or 20kHz, the accepted limit of human hearing. In digital audio we have to put a steep filter before the encoder to make sure nothing faster ever gets into the encoder. It is this filter that can cause audible issues and one of the main reasons why higher sample rate audio sounds more open and less closed off on the top end. Lastly bit depth. I wanted to spend a minute on this because there's a silly numbers game we all play to get more and more. CD's give us a dynamic range of 96dB based on its 16 bit depth. 16 bits was chosen because 100dB of dynamic range was considered perfectly adequate to handle the loudest to the softest passages of an orchestra if properly recorded. It also far exceeded the standard 60dB of dynamic range of tape recorders back when CD's came into play in 1982. Recent studies have suggested this number is probably too low and 120dB more adequately covers more than we can hear. But in our numbers game it is never enough and we moved on to 24 bits which gives us a whopping 144dB of dynamic range. We've all probably heard the difference between 16 bit CD's and 24 bit CD's and loved the differences. There are many reasons other than a lack of dynamics that causes us to appreciate the differences, but for the sake of argument let's just agree that 120dB is more than adequate for anything we're ever going to need and 144dB is overkill and giving us 24dB of added headroom. What of 32 bit? Since each additional bit gives us 6dB of added dynamic range, that's yet another 48 dB giving us a staggering 192dB of dynamic range. Overkill? You bet, and then some. This is way overkill and the penalty for this is much more data storage requirements and a tougher time decoding it - not to mention there are no DACS capable of reproducing that much dynamic range nor are there electronics or loudspeakers that can reproduce it. Let me close with a sobering perspective. 24 bit dynamic range can be expressed in more relevant terms we might understand as the loudness difference between a single sound molecule hitting our eardrum vs. the pressure of a jet engine blast. Think about that for a moment and ask yourself if you think we need more than this level of range. Tomorrow we begin the process of taking our PCM samples and converting them into music.
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