Wave Theory - Part 1

Apologies for the delay here. I started writing a number of things into this post, however it became a long, boring, technical marathon. So I'm going to break up these types of articles and post some interstitial things as well. I originally wanted to look at Quantization Noise, but there were so many concepts involved that I decided to start with the "Basics".


Superposition

Science and nature detest corners. Curves, even constantly varying ones, are much easier to deal with. This is because curves add together nicely through a principle called "Superposition." Long story short, curves can be added together and taken apart without any difficulty. 

If you've ever looked at music on an oscilloscope, you'll see a random squiggle that never seems to stop changing. Whilst it can make for an interesting visual effect, it's not very helpful. However, due to Superposition, we can break that seemingly random signal down into the component inputs. This is usually called the Fourier Function Transform, but you might be more familiar with the term "Spectrum Analyser." (I strongly advise not looking too deeply into it unless you really like maths.)

If you run a signal though a Spectrum Analyser, you change the random squiggle into a series of columns. Each column represents a frequency range; the height of each column denotes the amount that each particular frequency range is contributing to the original signal.

Input signals (Left) and the resultant Spectrum Analysis (Right)
Thanks Wiki Commons

Let's have a look at some pictures; because they are easier to understand than words.
The top picture is your standard sine-wave. Since there is only one frequency, the Spectrum Analysis shows us that information; one tall column. All of the power in this signal is contained within that narrow frequency range.

The second set of images shows static; a totally random signal at low level. If we look at the Spectrum Analysis, you'll see that the power is spread randomly across all frequencies. We'll get into the origins of static one of these days. Just not today.

The last set of images shows these two signals superimposed onto each other. At each point, the "height" of the two signals is added together to make the bottom left image. It's a bit hard to see in the image, but you'll note that the curve is no longer smooth. However, this is nearly impossible to tell by looking at the input signal.
However, when we look at the Spectrum Analysis, we can clearly see that most of the energy is still in that main frequency range, but there is energy spread out across the other frequencies.

This effect is normally called "Noise".

Repeating Patterns
There is one other cool thing about superposition.

Basically, any repeating pattern can be built up with the right combination of sine waves. Take, for instance, a square wave:

Once again, Thanks Wiki!

If you have a look at the above image, you'll see three lines.
The Red line is a "true" square wave. The Green-dashed line shows a Fourier Approximation of the square wave using 5 component waves. The blue-dashed line uses 15 component waves. These waves are superimposed onto each other, like this:

The left-hand images shows our four component waves and their relative powers. Just by looking at the left-hand side, we can see that the "Fundamental" frequency, which is the same as the frequency of the square wave, has the most power.

The second column shows the superposition, but without adding the waves together. The third column shows the resultant, superimposed wave. As we go down the list, it starts looking more and more like a square wave.

The right-hand column, again, is what you'd see if you put the signal into a Spectrum analyser. There's a couple of points to note here:

•  For a square wave of a fundamental frequency F, the frequency of the component waves (f) is as follows - f = (2n+1)F, where n starts at 0 and goes to infinity
•  The power of each wave drops off significantly as n gets bigger (or, to put it another way, as the frequency of the component wave goes up, the power of that component goes down).

It turns out that once you get past n=16 or so, the power in the higher frequencies is so low that it no longer matters if you include them or not.



Next Time
It is very tempting to plough ahead here and talk about why I just wrecked your mind with superposition, but I won't.

Here's a hint though, it has to do with square waves and noise, and why digital and analogue aren't all that different.

As always, please feel free to post questions in the comments section!

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.

1.5 Mile Wireless connection

Just saw this pop up on Engadget. Wireless repeaters that go for 1.5 miles (2.4km).

I'm thinking large stadia or live sites where you'd need to move a bunch of signals around but it would be impractical to run Cat5 across the ground, or events like the Sydney New Year's Eve fireworks where there are barges spread out across the harbour...

Press-release and first thoughts:
http://www.engadget.com/2011/10/24/amped-wireless-gives-your-wifi-1-5-mile-range-never-lose-signal/

Company Signal:
http://www.ampedwireless.com/

Layers of the Internet - Part 4

If you are new to this area, or are looking for the first three parts of this series, please use the following links:
Layer 1 - Link Layer
Layer 2- Internet Layer
Layer 3- Transport Layer

To recap quickly, the Link layer is the physical connection between devices (be it wireless, electrical or optical).
The Internet Layer is the layer that deals with the virtual separation of the entire Layer 1 network into smaller, virtual networks, and also allows traffic to be routed from one side of the planet to another.
The Transport Layer deals with two main things; where the data goes inside the devices that receive it, and also how the packets are passed around the networks (e.g. error correction protocols - re-sending a packet that never arrived at the destination.


Layer 4 - The Application Layer
For a second, let's think about what we are trying to achieve with a data network. We are trying to move information (be it computer data, an image, live audio... anything) from one point to another. If we look at what we've done in layers 1-3, we can see that we've done nothing but move the data from one end of the earth to the other.

Layers! Layer 4 is like the river and the clouds above; they rely on the lower layers of the earth, but they don't really care about them

.
But before any data can be delivered, we have to actually work out what data we are going to transport, why we around going to transport it and then what we are going to do with it at the other end. Data is useless unless we actually do something with it. For example, you could send a friend a photo, but if they can't view it then there was no point to transferring the data in the first place.

This is where the application layer comes in. It is the layer of the Internet that interfaces with the Users, but it is also the layer where we actually change the information that we are sending.

But Layer 4 isn't all about the Users, there's a lot of background processes involved. Let's have a quick look at a simple internet action; checking this blog:

• Step 1: You open your browser and type "http://arts-comms.blogspot.com". This is the start of the process; you enter a small amount of data; 30 characters. It's not much when you think about it.

• Step 2: Your browser tries to find the address of this page. If you were going to send a letter to a friend you couldn't just write their name on an envelope, post it, and hope for the best. The "Human-readable" Universal Resource Locator (URL) is similar to you friend's name; you can use it to describe them and look them up, but it isn't exactly an address. So, before your browser starts downloading this page, it looks out for a Domain Name Server (DNS) that will translate the URL into a TCP/IP Address.This address combines the Layer 2 and 3 addresses for the webpage. In this case the IP part of the address is 74.125.71.132, and the port is 80. This could be written 74.125.71.132:80.

• Step 3: Your browser now requests a session with the blogspot.com webserver. Now that your browser knows where to look, it will send a request to 74.125.71.132:80 to ask if it can start talking to the Server. The server will normally check that there are no bans on your device, or any other reasons that it wouldn't want to talk to you.

• Step 4: The Server opens a port and allows a session to begin. Should everything in Step 3 check out, the server will allocate a port number (this can be random, or fixed; it depends on the server) and then sends the information to your browser, letting it know that it's all good to go.

• Step 5: Your Browser requests the Webpage. Now that the Server and your browser are talking, the browser finally asks for this page, sending along with the request any additional information that might be required (e.g. your login details, or which exact page you're requesting).

• Step 6: The Server retrieves the webpage from its hard drive, and then transmits it as a series of packets. If you were to send a entire webpage as a single packet, it would be huge, and that would slow it down through the Internet. So the Server splits up the webpage into a number of small packets, adds a bit of information to let your browser know the order of the packets, and then transmits them through the network.

• Step 7: Your browser assembles the webpage, checking for errors as it goes. There is always a chance that some packets will get lost in transit. However, since the server has added information for your browser, it will know if anything is missing. If something doesn't make it then your browser will re-request the missing pieces.

• Step 8: Close the Session. Once everything has been checked, and you're happily reading away, the browser sends a message to the Server to finish off the session that was opened in Step 4. Once this is closed the connection disappears from the internet.

So, from your 31 keystrokes (including the "enter" key at the end) your browser and the Server have been communicating at Layer 4. You'll notice that I barely mentioned the Layer 1-3 protocols; and that is because  at Layer 4, just like all of the layers below it, the lower levels are transparent. It doesn't matter that I'm on a wireless connection and the server is on a optical fibre connection; they are connected up to Layer 3, and that's all that matters.

I'll be doing little write-ups on the various protocols as I continue to write this blog, so please stay tuned to the Glossary. Once I write an article on each protocol I will link it from the Glossary.

Layers of the Internet - Part 3

Before I start I would like to make a minor classification.
The "Layers" to which I am referring are the Internet Protocol layers, as specified in RFC 1122. I feel this model is more appropriate to the topics that I cover in this blog.


For those of you that wish to delve further into Networking as a subject, please refer to the Open Systems Interconnection (OSI) model. This model is the one that you would study in a networking degree, however it is slightly too specific for the purposes of this blog.




Layer 3 - The Transport Layer
In the previous two parts of this section of the blog, we looked at Layer 1 - The Link Layer and Layer 2 - The Internet Layer. In those layers, we say that each device was physically connected to all others, but with a bit of technology, we could divide up that huge network into smaller little sections.

I'll admit, it's difficult to visualise the Transport Layer. Here's some model trains.

As we have now connected on Layers 1 and 2, we can assume that our two devices are talking to each other. At this point it doesn't matter how that happens, or how many switches the packets have gone through in order to get from A to B. The tunnel through the Internet has been made, and for all intents and purposes, it isn't broken until the connection is shut off.

Layer 3 tells us two things; how a packet will move through a network, and where it will go when it gets there. In order to understand this we will examine two of the main Layer 3 Protocols, Transmission Control Protocol (TCP) and the User Datagram Protocol (UDP). And yes, if you noticed that the "TCP" looks very similar to the "TCP" in "TCP/IP", you'd be correct. Since TDP is the most common Layer 3 Protocol, and IP is the most common Layer 2 protocol, people refer to this model as the TCP/IP suite of protocols. However, due to the complexity of the protocol, I will start off with the UDP.

User Datagram Protocol
Take a moment to think about how many different network-enabled programs you are running now. On my machine I have two browsers with a few tabs in each, Skype, two email clients, a couple of automatic software updaters.... the list goes on. Now think about a lonely packet headed my way. It has the MAC address (from Layer 1) so it knows where my computer is. It has my IP address (from Layer 2) so it knows how to find me on the network. But once that packet finds its way into my wireless adaptor, where does it go? Is it a part of a webpage, or a message from a friend via Skype, or an email?

Both the UDP and TCP use a number, called a "Port," to direct a packet to the program that it needs to arrive at. Your network adaptor reads the Port number and forwards the data to the appropriate program for processing.

A UDP packet contains a bit of information that identifies it as a UDP packet and a Port number. That's about it. The advantage of this is that you have a smaller packet, which means faster transmission times. We'll look into this a bit later.

Transmission Control Protocol
Whilst a UDP packet basically only has the Port number, a TCP packet contains a lot of additional information. TCP packets can contain information relating to tracking and delivery protocols. For example, a TDP packet could identify that it was the 15th packet in a sequence, and that the receiving device should send notification of receipt.

This information can be used to make sure that packets that have been lost due to network errors can be re-requested and re-transmitted. Packets that take too long can killed off. Devices can send packets to each other to check the speed and path of the transmission.

All of this extra information makes the packets bigger, and hence slightly slower. However, in any non-real-time application this extra transmission time doesn't make much difference. Since very few transmissions actually require real-time transmission, the more Robust TCP is more common than UDP.

The main place we see UDP packets in the Arts industry is in audio/video transmissions, like Dante or AVB.  UDP also requires less programming, and thus it is more common in smaller applications, so you may come across UDP systems in some control software.

"Layer 3 Switches"
Normally a switch will read the Layer 2 information (the IP Address) in order to find out where to send the packet. As we saw in the Layer 2 article, this is used to prevent every device receiving every packet on the network. If a switch only does this, then it is known as a Layer 2 switch.

However, some switches can be programmed to read the Layer 3 information. Switches can read the TCP information to adjust flow control (e.g. if the switch is over capacity, it can request the sending device to slow down the transmission rates). This can also allow for the ability for a switch to send more important packets before standard packets (e.g. Telephone or real-time audio is transmitted before a webpage).

Interesting Enagadget article on Whitespace

http://www.engadget.com/2011/09/16/fcc-to-test-white-space-database-at-its-own-pace/

I know that I have been hoping to drip-feed information here, but occasionally I will need to jump the gun.

For those of you that don't know about the "White Space," it is referring to the spaces in the RF Spectrum that will be left between Television Channels, leaving clear bandwidth for devices to communicate on.

This spectrum remains unlicensed, and thus manufacturers can use this space for data transfer. Wireless Microphones operate in the same space; they are designed to work in the TV channel space, but in the "gaps" between channels. Of course, the introduction of more "White Space" devices sends shivers up most Radio Mic Technician's spine, because it potentially means that a device will suddenly appear in the middle of your spectrum... when you least expect it!


The reason White Space Devices didn't work so well in the past is due to the difference between Digital and Analogue TV transmission. Analogue is much less predictable, however Digital Channels stick out like a sore thumb to even the most basic devices. So, when you turn off the Analogue stations, you make it a lot easier to make White Space Devices.

It shouldn't be confused with the Digital Dividend, which is the space at the high end (~800MHz) of the spectrum that will be "empty" (i.e. no TV channels) once the Analogue TV stations are turned off. This spectrum will be sold off, and in the US it made a hell of a lot of money.

I will go into all of these topics in much greater detail, but for those of you that are hanging on any bit of Spectrum Information, please enjoy the link.

The layers of the Internet - Part 2

The Internet Layer
In the last post I explained the basics of Layer 1 of the Internet Protocol; the Link Layer.

The Link Layer is where all devices are physically connected, either by wireless (e.g. Wireless LAN or 3G) or by a wired (e.g. Ethernet "Blue String" or ADSL) connection.

Whilst this is a great concept, if every device were to receive all of the data transmitted on the Internet, then we would be slowing down the process beyond belief.

Enter Layer 2 - The Internet Layer

This is Layer 2

On a network drawing, a network was always drawn using standardised symbols. Since everything that was on the "Internet" was connected at Layer 1, it no longer mattered how things were connected. You only had to show that there was some kind of connection.

And so the network symbol for the "Internet" became a cloud. It was some ethereal entity, floating out of the reach of Network Administrators across the globe.

Unfortunately marketing departments caught hold of this analogy, and thus Cloud Computing was born. You can see the "Cloud", and it brings you good things (like shade, and rain for your crops) but you have little to no power over it. It's there whether you like it or not. 

So how does it work?

Packet-Switching Networks

In this previous blog post I explained the anatomy of a standard Internet Protocol (IP) Packet. Packets are the currency for IP networks, and indeed the entire Internet. Without repeating myself too much, they contain two main parts; a "Payload" (the data that you want to move around the network) and a "Header" (which contains the addresses relevant to the Data).

In order to understand how the Internet works, we are going to have to introduce our first specific piece of network hardware: the Switch.

The image above is that of a "Switch," and it is a common thing to be found in data centres across the world. However you are reading this blog, somewhere along the line you are connected to a Switch. It might be a little 4-port switch that came with your ADSL plan, or you might be connected to a commercial-grade switch (like the one above) at work.

Switches are the building blocks of the Internet, and they elevate matters from Layer 1 (Link Layer) to Layer 2 (Internet Layer).

Every blue or pink cable in the above image connects to a device; a telephone, a computer, a printer etc. This is the Layer 1 connection. You can tell they are working by the blinking green lights. The Orange cables connect those switches to other switches, which the connect to other switches... until they reach whatever destination they need to get to. These connections are called "Uplink Ports", as they are headed up towards the "Cloud".

When a packet is sent to a switch, it "opens" it up and reads the "Header" (not the "Payload"). In the "Header" is all of the addressing information that the Switch needs to send the packet to where it needs to go. If the destination address is connected directly to the switch, then the packet will be sent directly to that device. If not, then the switch will send the packet to the "Uplink" port, at which point the next Switch will repeat the same process until the packet arrives at its destination.

By doing this, Switches make sure that you only receive the packets that you need to read your emails, browse your websites, control your motors, or route audio. Switches don't care what your packet has in it, so long as the address in the Header is valid.

The address used by the Internet Layer is the Internet Protocol (IP) Address. I will go into (much) more details about IP Addresses in a later post as the topic is as broad as the Internet itself. Suffice to say, a common IP address is an 8-byte address, usually rendered in four groups of numbers from 0 to 255, e.g. 192.168.0.254.

Once two devices are connected at Layer 2 they are considered "Networked" and can now communicate as if they were in the same room. Layers 3 and 4 deal with how they communicate, and we will cover these in the next blog post.