Sunday, 9 June 2019

Analog & Digital Graphing

Well, before we start looking at how we can convert sounds into the electrical pulses that are required to send it along the cables that make up the network, let us consider a few more of the basic things that make up the network. Firstly we will start off with the actual cables, of which there are three types: twisted pair, coaxial, and fibre optic.

Twisted Pair: A twisted pair cable is basically what the name sounds like - two insulated copper wires twisted about each other. The advantage is that they are cheap, but the disadvantage is that not only are they slow, but they really can't send all that much along them - sort of like a really narrow pipe for pumping water. Also, you really don't want to have them running for any really long distances, or even a medium distance for that matter.

Coaxial: This is another form of copper wiring, and is what is generally referred to when people talk about the copper network, particularly when we are talking about the NBN. Look, they are perfectly fine for sending analogue voice signals, but when it comes to high speed broadband, well, they sort of aren't suited for that purpose at all. Basically it is an inner conducting wire, surrounded by insulating material, which in turn is surrounded by a metallic shield, and finally surrounded by another insulating material. ,

By Tkgd2007 - Own work, CC BY 3.0

Fibre Optic: Well, these are the cables that are considered to be at the forefront of data transmission technology. Okay, fibre optic cables have been around for a very long time, but the thing is that they are able to carry huge amounts of traffic at a very high speed. Basically they consist of cables made of glass that are insulated. In fact they will contain multiple cables bundled together. They are also very useful for sending signals long distances, and do so by bouncing the photonic signals along the cable (fibre optic uses light as opposed to electricity as a medium).

The above is what is known as guided media, namely because the signals are guided along a wire. However, we also have unguided media, which is basically radio signals sent across the, well, air. They will normally be sent from a transmitter and picked up by a receiver. The signals will be converted to electro-magnetic signals at the transmitter, and the receiver will pick it up and convert it back.

So, now let us consider the difference between digital and analogue. Basically analogue data takes of a continuous value that changes smoothly over time. Analog signals are measured in hertz (hz), otherwise known as cycles per second. Digital data takes on discrete values, usually in the form of 0s and 1s (and all the other variations that I keep on throwing up). Digital transmission is measured in bits per second. The table below shows an analogue signal on the left and a digital signal on the right.

Analog Graphs

Now, back to sine waves for a bit - they can be measured in either the time domain, or in the frequency domain. As pointed out, frequency is basically cycles per second, so a sine wave, when measured on the frequency domain, will appear different to one that appears on the time domain, as shown below:

Now, the reason we have come back to this is not so much to look at the wave on the time domain, but rather on the frequency domain. The reason for this is because it takes us into the realm of spectrum. The spectrum is the range of frequencies that the signal occupies, and if a number of signals are placed onto a chart along the time domain, we simply come up with a jumble of squiggles. However, if we place it on the frequency domain, we will be able to read it much better. The frequency domain is actually much more useful, and clearer, when it comes to reading multiple sine waves, as the diagram from my lecture notes below shows:

This is particularly useful when the three sine waves have been combined because they will actually produce something different. However, this brings us to the concept of bandwidth, which is basically the width of the spectrum. To calculate a signal's bandwidth, you subtract the highest frequency from the lowest frequency, as the diagram (from my lecture notes) below demonstrates:

So, if we have a sine wave (or actually three sine waves melded together) with frequencies of 100 hz, 300 hz, and 500 hz, and maximum amplitudes of 10 v, 3 v, and 1 v, then the bandwidth would be 500 - 100 = 400 hz, and the frequency graph would be as follows:

Digital Graphs

Well, now that we have considered the analog graphs, let us now turn to digital graphs. First, let us look at the graph:

Now, the bit interval is actually the inverse of the bit rate. So, if we have a bit rate of 2000 bps (bits per second), then the bit rate is 1/2000s = 0.0005 s = 500 μs (micro seconds).

So, now that we have the graphs, next we will move on to sampling.

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Analog & Digital Graphing by David Alfred Sarkies is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. This license only applies to the text and any image that is within the public domain. Any images or videos that are the subject of copyright are not covered by this license. Use of these images are for illustrative purposes only are are not intended to assert ownership. If you wish to use this work commercially please feel free to contact me

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