Yesterday we explained how we take snapshots or pictures of the changing voltage stream known as analog. Each picture is actually a single voltage measurement at a fixed point in time. Once we've measured the voltage we convert that measurement to a numeric value and store the value. Each stored value is called a word.
Each snapshot is called a sample. 44.1kHz sample rate means we're taking 44,100 voltage samples per second, converting them to a numeric value and storing that value on our hard drive or optical disc.
But we're all familiar with CD's being expressed in this fashion: 44.1kHz 16 bit. So what's the deal with the number of bits? Granularity and size.
If I have 4 bits I am limited to only 16 numbers that I can use to measure the voltage of each sample. Most CD players output 2 volts at maximum so this means that I can only have 16 steps of 0.125 volts each. Because analog is a continuous signal without these gross steps, my result with music would be pretty awful.
However, if I use a 16 bit system I now increase the fineness of those steps to65,536 instead of 16. And if I go to a 24 bit system I get a whopping16,777,216 possible numbers. 32 bits gives me even more,4,294,967,296 possibilities.
So the sample rate determines how many times I take a voltage measurement and the number of bits determines how fine those measurements are. The more bits the closer to perfect I can record the voltage measurements as well as how large the voltages range is. In terms you're probably more familiar with, this increased granularity can be expressed in terms of magnitude which we know as dynamic range.
Dynamic range is the difference between the loudest and the softest and increases by 6dB for every bit. 16 bit audio has 96dB of dynamic range while 24 bit audio has a whopping 144 dB of range. The best ears on the planet can handle about 124 dB of dynamic range and anything greater than that is generally wasted. In fact, one of my pet peeves is that 24 bit audio wastes dynamic range on us when we could use it for finer granularity and accuracy instead - but that's a whole other story.
So to sum up this small part of PCM (yeah, there's much more to go), the sample rate determines the maximum limit to what we can record in terms of frequency while the bit depth determines the size and/or granularity of what we measure. Sample rate limits are half of the rate itself: 44.1kHz can accept audio up to 20kHz, while 192kHz can handle up to 96kHz.
Even though human hearing generally doesn't exceed 20kHz, higher sample rates reduce the need for nasty filters and generally sound far better than CD limitations.
