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Signals

Sub-topic Outline:

• Types of Signals
  • Analog vs Digital
  • Periodic vs Non-Periodic
• Simple Analog Signals
• Complex Analog Signals
• Digital Signals
• Bandwidth Capacity

Analog and Digital Signals

• Basis of all computer networks: electromagnetic signals transmitted across some physical media
• Analog signals - can have any value in a continuous range. Eg. any value between 0 and 1
• Digital signals - can only have discrete values. Eg. 0, 0.5 and 1

Graphical Representation of analog and digital signals:

Periodic and Non-Periodic Signals

• Periodic signals - values is in repeated patterns
• Non-Periodic signals - no repeated patterns in the signals

Graphical Representation of periodic and non-periodic signals:

Simple Analog Signals

• The most fundamental periodic signal can be represented by a sine wave.
• The sine wave has three components:
  1. Amplitude
     • height of the signal wave
     • measured in volts, amps, or watts
  2. Frequency
     • the number of cycles per seconds
     • measured in Hertz (Hz)
  3. Phase
     • the position of the waveform relative to time 0

Graphical Representation of amplitude, frequency (don't worry about the concept of phase):

Complex Signals

• Complex signals can be formed by adding together a collection of sine waves.
• We use Fourier Analysis to decompose the complex signal to find which sine waves make up the complex signal

Graphical Representation of adding two sine waves of different frequencies to form a more complex wave:

Digital Signals

• In digital signals,
  • Amplitude takes on the values 0 or 1
  • Frequency becomes the bit rate (how fast the 0's and 1's are coming through)
  • Phase remains the same concept

Approximating Digital Signals

• Digital signals can be represented as a series of component sine waves (called sub-harmonic components) of different frequencies (through Fourier Analysis).
• To get a perfect digital signal, we need an infinite number of component sine waves.
• The more component sine waves we have, the better our digital signal.
• So (the key to remember for now!):
  • The more complex the wave, the more component sine waves we need.

An Example of Sending Digital Signals through an Analog Medium

We will use Fig 2-1 in the textbook to illustrate.

We have a medium capable of transmitting signals. In this example, we will use voltage (in volts) to transmit our data. We can use other measurable properties, such as current (in amps), or power (in watts). So the steps are:

1. We first need an encoding representation for our data. Say we use normal 8-bit ASCII representation, which means a character "b" is 01100010. We want to transmit this binary sequence 01100010 down the line.
2. What we want to do is to send the signal by changing the voltage on the line. But we have to decide on a regular interval, or else the receiver won't know if 0.5 seconds of 1 volt means 1, or 11, or 111, etc. So we decide on our baud rate, which is the number of changes to the signal per second. Say we change the voltage once every 0.1 seconds. So our baud rate is 0.1. In this case, we can send 10 bits per second (bps). Note that we can send more than 1 bit with every signal if we want, but we need to have more than just 0 or 1 as our voltage values. Say if we have four possible voltage values (0, 1, 2, 3, 4) we can send 2 bits with every voltage signal, by taking 0 volts = the bits "00", 1 volt = "01", 2 volts = "10", 3 volts = "11". In this case, since we can send 10 signals in a second and each signal has two bits, we can send 20 bps. How many different voltage values we can use depends on the equipment.

3. So now we send our voltage signals down the line, and in a perfect world with no lost of power, the other side will get the EXACTLY the voltage values we send. Unfortunately, this is not a perfect world, and ALL lines loses power. To decide on what happens to a signal when some power is lost in the line, we need Fourier Analysis.

Remember from above that we said a digital signal such as Fig 2-1(a) can be approximated by a complex analog wave made up of component sine waves of different frequencies. Each of those components will have a different strengths. Say we give all the components an index number 1, 2, 3, ... The component numbers which are low means the component wave have low frequencies, and components with high indices have high frequencies. On the right in Fig 2-1(a) is a graph of this. Each component wave (the index called "harmonic number") is has a strength. Some are high, like the 2^nd harmonic. Some are low, like the 8^th harmonic.

Why do we need to know what components waves make up the original signal we send? Because when a signal loses power, the high frequency components, with high index numbers, gets cut off (or attenuated). So for us to determine if a line can transmit in high enough frequency, we need to look at our original signal composed ONLY of it lowest frequency components. For example, if the line can only transmit in the one lowest frequency, we will have the signal in Fig 2-1 (b). This is hardly good enough, since the signal values (ie. amplitude) is about the same throught-out. We can hardly tell where the 0's are and where the 1's are.

On the other hand, if the line can support the frequency up to the 8^th harmonic component, our receiver will get the signal as shown in Fig 2.1(e). This is good enough, since at time 0, the amplitude is about 0, at time 0.1 sec (remember we are using 0.1 sec as our interval in this example) the amplitude is almost 1, at time 0,2 sec the amplitude is almost 1, and so on. We can approximately get back the original signal of 01100010.

So if we happen to have a line that can transmit up to the 8^th harmonic component, we can send the 01100010. If the line can't, then we can simplify the wave form by sending less number of bits in the same amount of time.

Eg. Transmitting only the the four bits in the same amount of time



means a simpler wave form, and so don't need as much high frequency components to represent compared to the original



Nyquist have worked out based on a line's bandwidth (how high the frequency it can transmit) and the number of different digital values we can have, exactly what the maximum data transfer rate of the line is. Shannon have also worked out the same, but considering the ratio of noise to signal of the line as well. Their results and formulae are presented in the book Sec 2.1.3. In this unit, you are not required to know the formulae or how to use them, just keep in mind these formulae exists. Those motivated who wants to understand the theorems can read the text and approach me for further elaborations.

4. Once the signal is sent, the receiver only needs to detect the voltage coming through the line at the regular interval (0.1 sec) we decided on, and work out the original set of 0's and 1's.

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