Pulse-Code Modulation - Music to our ears

Okay, so we've just spent a lot of time looking at how data moves around a network. I hope that you were all with me for the ride. If not then please feel free to comment on any of the posts and I'll answer your post.

For the next couple of weeks I'd like to start looking at the data that you actually put into those packets.

One of the easiest places to start looking at digital signals is the humble Pulse-code Modulation, or PCM, method of encoding analogue information into a digital signal.

Analogue vs Digital
No, I'm not going to get into the "aesthetic" differences between analogue and digital, save to say that the only instrument that you can trust is your own ears. If it sounds better to you, then it sounds better to you.

I would like, however, to clarify something quickly. An "Analogue" signal is a proportionate signal with no real limitation. The local air pressure around a microphone or a signal can be measured by a device and turned into an electrical signal that is proportionate to the pressure. The higher the pressure, the higher the voltage. The voltage is an "Analogy" of the pressure.
This is what we refer to as an "Analogue" signal. Most simple electronic devices will process and run on analogue signals.
At some point, everything is an "Analogue" signal; the pressure changes that reach your ear drums or the light changes that reach your retinas are "Analogue".

A "Digital" signal, however, is somehow encoded so that it is no longer proportionate to the original signal. Through some kind of electronic process the Analogue signal is broken down into symbols of some kind that are readable only by devices that use that format. Before we can interact with them again then they need to be converted into an Analogue signal again. This process is called "Encoding" (Analogue to Digital) and "Decoding" (Digital to Analogue). Combine "enCOder" and "DECoder" and you get CODEC... but we'll get to those later.

Pulse-Code Modulation
Anyone who's ever Google'd "Digital Audio" will have seen a picture similar to this one:

Let's assume that we are looking at the Encode (Analogue to Digital) side of things (although the process is exactly the same in reverse).
The red line is our input signal; a standard sine-wave. This could be anything;  an audio signal, the number of people that like or dislike the current Prime Minister... it doesn't matter. We have a signal that is changing as time goes on.

The analogue signal is continuous and unbroken.

Pulse-Code Modulation sets a value (shown above as 0-15) for each equivalent amplitude. To convert the signal into a digital one, we record the value of the analogue signal at the start of each of the time divisions shown along the bottom access. This process is called "Sampling" - you are taking a sample of the Analogue signal at each of the time divisions.

You'll note that on the image above you can see a difference between the continuous Analogue (Red) signal and the Digital (Grey) one. It looks like a lot, right? In fact, the small differences in images like the above are one of the main arguments used by Analogue supporters. However, there is something missing from this picture...

Bit Rate
The picture above gives you a pretty good look at what you'd see in a phone-line; a 4-bit system. A bit is a single binary "symbol". One bit gives two states; two bits gives four, three bits give eight and four bits give sixteen states.
The number of "bits" that a digital signal contains is referred to as the Bit Depth. In basic terms, the higher the bit depth, the better the quality.

Even your most basic audio (CD-quality) has a bit depth of 16 bits; or about 65 thousand different states. The Human ear isn't really able to detect that kind of resolution; it would be like trying to look at the millimetre markings on a ruler that was 10 meters away.

Still, there are higher bit depths; standard digital audio (AES/EBU-3, which I will cover in a future article) runs at 20 bits (1,048,576 states) or at 24 bits (16,777,216 states). At this point, you're pretty much splitting hairs with a 2000-pound bomb...

But there is another factor that affects the quality of the sound; the rate at which the audio is sampled.
As a general rule, you want to take a sample at twice the frequency of the highest frequency you want to hear. The label on a new-born baby reads 20Hz-20,000Hz, although by the time you've used an MP3 player and gone to a concert or two you will be lucky if you can hear above about 17,000Hz.
Thus, the main sampling rate used in digital audio is 44.1kHz (CD-quality). "Professionals" will use 48kHz, or even go as high as 96kHz. Once again; at that level you are recording detail that humans just can't perceive. It's like taking a photo in ultraviolet; it might look brilliant, but there is no way for us to see the result.





I would like to continue this article, but in the interest of keeping things concise I will hold off for the time being. Next article I will look at a couple of the strange effects of PCM, and how we avoid them.
But for now, I must away. Until next time.