Data Communications and Networking

Data Communications and Networking Chapter 3: Data and Signals

Data and Signals What is Data? Data is information that has been translated into a form that is more convenient (easy) to move or process. Relative to today's computers and transmission media, data is information converted into binary digital form.

Data and Signals What is Signal? A signal is an electric current or electromagnetic field used to convey data from one place to another.

Data and Signals One of the major functions of the physical layer is to move data in the form of electromagnetic signals across a transmission medium. Generally, the data usable to a person or application are not in a form that can be transmitted over a network. To be transmitted, data must be transformed to electromagnetic signals. 1. Analog and Digital Both data and the signals that represent them can be either analog or digital in form.

Analog and Digital 1.1. Analog and Digital Data Data can be analog or digital. The term analogdata refers to information that is continuous; digital data refers to information that has discrete states. For example, an analog clock, that has hour, minute, and second hands gives information in a continuous form; the movements of the hands are continuous. On the other hand, a digital clock that reports the hours and the minutes will change suddenly from 8:05 to 8:06.

Analog and Digital • Analog data, such as the sounds made by a human voice. When someone speaks, an analog wave is created in the air. This can be captured by a microphone and converted to an analog signal and converted to a digital signal. • Digital data is data stored in computer memory in the form of 0s and 1s. They can be converted to a digital signal or modulated into an analog signal for transmission across a medium. Data can be analog or digital. Analog data are continuous and take continuous values. Digital data have discrete states and take discrete values.

Analog and Digital 1.2. Analog and Digital Signals Like the data they represent, signals can be either analog or digital. • An analog signal has many levels of intensity over a period of time. As the wave moves from value A to value B, it passes through many number of values along its path. • A digital signal, on the other hand, can have only a limited number of defined values. Although each value can be any number, it is often as simple as 1 and 0.

Analog and Digital

Analog and Digital In data communications, we use analog signals (periodic) and digital signals (non-periodic). 2. Analog Signals Analog signals can be classified as simple or composite (combine). • A simple periodic analog signal, a sine wave, cannot be decomposed into more simple signals. • A composite periodic analog signal is composed of multiple sine waves.

Periodic Analog Signals 2.1. Sine Wave The sine wave is the most fundamental form of a periodic analog signal. When we visualize (imagine) it as a simple oscillating curve. Figure below shows a sine wave. Each cycle consists of a consistent value.

Periodic Analog Signals A sine wave can be represented by three parameters: the peak amplitude, the frequency, and the phase.

Periodic Analog Signals 2.1.1. Peak Amplitude The peak amplitude of a signal is the absolute value of its highest intensity, proportional (~) to the energy it carries. For electric signals, peak amplitude is normally measured in volts. Ex: The power in your house can be represented by a sine wave with a peak amplitude of 155 to 170 V.

Periodic Analog Signals

Periodic Analog Signals 2.1.2. Period and Frequency Period refers to the amount of time, in seconds, a signal needs to complete 1 cycle. Frequency refers to the number of periods in 1 s. • (Frequency = cycles per second) Note that period is the inverse of frequency, and frequency is the inverse of period, as the following formulas show.

Periodic Analog Signals Period is formally expressed in seconds. Frequency is formally expressed in Hertz (Hz), which is cycle per second. Units of period and frequency are shown in below table: Units of period and frequency

Periodic Analog Signals Example 1: The power we use at home has a frequency of 60 Hz. The period of this sine wave can be determined as follows:

Periodic Analog Signals Example 1: The power we use at home has a frequency of 60 Hz. The period of this sine wave can be determined as follows: This means that the period of the power for our lights at home is 0.0166 s or 16.6 ms.

Periodic Analog Signals Example 2: Express a period of 100 ms in microseconds. Solution From the table we find the equivalents of 1 ms (1 ms=10−3 s) and 1 s (1 s= 106μs). We make the following substitutions:

Periodic Analog Signals Example 2: Express a period of 100 ms in microseconds. Solution From the table we find the equivalents of 1 ms (1 ms=10−3 s) and 1 s (1 s= 106μs). We make the following substitutions: or 1ms= 103 μs100ms= 100.103μs= 105μs

Periodic Analog Signals Example 3: The period of a signal is 100 ms. What is its frequency in kilohertz? Solution First we change 100 ms to seconds, and then we calculate the frequency from the period (1 Hz = 10−3 kHz).

Periodic Analog Signals 2.1.3. Phase and phase shift The term phase describes the position of the waveform relative to time 0. If we think of the wave as something that can be shifted backward or forward along the time axis, phase describes the amount of that shift. It indicates the status of the first cycle.

Periodic Analog Signals 2.1.3. Phase and phase shift Phase is measured in degrees or radians [360° is 2πrad; 1° is 2π/360 rad, and 1 rad is 360/(2π)], with 360 degrees being one complete cycle. The beginning of a wave is 0 degrees; the first peak is 90 degrees (1/4 cycle), a phase shift of 180° corresponds to a shift of one-half of a period (1/2 cycle) and the end is 360 degrees.

Periodic Analog Signals 2.1.3. Phase and Phase Shift Three sine waves with the same amplitude and frequency, but different phases

Periodic Analog Signals Looking at Figure above , we can say that 1. A sine wave with a phase of 0° starts at time 0 with a zero amplitude. The amplitude is increasing. 2. A sine wave with a phase of 90° starts at time 0 with a peak amplitude. The amplitude is decreasing. 3. A sine wave with a phase of 180° starts at time 0 with a zero amplitude. The amplitude is decreasing. Another way to look at the phase is in terms of shift or offset. We can say that 1. A sine wave with a phase of 0° is not shifted. 2. A sine wave with a phase of 90° is shifted to the left by 1/4 cycle. 3. A sine wave with a phase of 180° is shifted to the left by 1/2 cycle.

Periodic Analog Signals Example: A sine wave is offset(shift) 1/6 cycle with respect to time 0. What is its phase in degrees and radians? Solution We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is:

Periodic Analog Signals 2.1.4. Wavelength Wavelength is another characteristic of a signal traveling through a transmission medium. The distance between peaks (high points) is called wavelength.

Periodic Analog Signals If the propagation speed (the speed of light) and the period of the signal are given, Wavelength can be calculated via below formula: Wavelength = Propagation Speed x Period = Propagation Speed x (1/Frequency) = Propagation Speed / Frequency We represent wavelength by λ, propagation speed by c (speed of light), and frequency by f. λ = c/f Where: λexpresses in m ; c is 3*108 m/s

Periodic Analog Signals For example 1: The wavelength of yellow light (frequency = 5 x 1014 Hz) in air is: λ = c/f = (3 x 108)/(5 x 1014) = 0.6 x 10-6 m = 0.6 µm For example 2: The wavelength of red light (frequency = 4 x 1014 Hz) in air is: λ = c/f = (3 x 108)/(4 x 1014) = 0.75 x 10-6 m = 0.75 µm

Periodic Analog Signals 2.1.5. Time and Frequency Domain The time-domain plot shows changes in signal amplitude with respect to time (it is an amplitude-versus-time plot). A frequency-domain plot shows changes in signal amplitude with respect to frequency.

Periodic Analog Signals 2.2. Composite Signals A single-frequency sine wave is not useful in data communications; we need to send a composite signal which is a signal made of many simple sine waves. In the early 1900s, the French mathematician Jean-Baptiste Fourier showed that any composite signal is actually a combination of simple sine waves with different frequencies, amplitudes, and phases.

Periodic Analog Signals The amplitude of the sine wave with frequency f is almost the same as the peak amplitude of the composite signal. The amplitude of the sine wave with frequency 3f is one-third of that of the first (f/3). The amplitude of the sine wave with frequency 9f is one-ninth of the first (f/9). Frequency of first sine wave is 3Hz, therefore the frequency of second sine wave is 9Hz and the third is 27Hz.

Periodic Analog Signals 2.3. Bandwidth • In computer networks, bandwidth is often used as a synonym for data transfer rate - the amount of data that can be carried from one point to another in a given time period (usually a second)-bps. In general, a link with a high bandwidth is one that may be able to carry enough information. • In electronic communication, bandwidth is the difference between the highest-frequency signal component and the lowest-frequency signal component. Since the frequency of a signal is measured in hertz BW (Hz).

Periodic Analog Signals 2.3. Bandwidth For example, if a composite signal contains frequencies between 1000 and 5000, its bandwidth is 5000 - 1000, or 4000. Note: The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal. B = fh - fl

Periodic Analog Signals Example1: If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V. Solution

Periodic Analog Signals Example1: If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V. Solution Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then

Periodic Analog Signals The spectrum has only five spikes (points), at 100, 300, 500, 700, and 900 Hz

Periodic Analog Signals Example2: A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? Draw the spectrum if the signal contains all frequencies of the same amplitude. Solution

Periodic Analog Signals Example2: A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? Draw the spectrum if the signal contains all frequencies of the same amplitude. Solution Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then

Periodic Analog Signals The spectrum contains all integer frequencies. We show this by a series of spikes

Periodic Analog Signals Example3: A signal has a spectrum with frequencies between 1000 and 2000 Hz (bandwidth of 1000 Hz). A medium can pass frequencies from 3000 to 4000 Hz (a bandwidth of 1000 Hz). Can this signal faithfully pass through this medium? Solution:

Periodic Analog Signals Example3: A signal has a spectrum with frequencies between 1000 and 2000 Hz (bandwidth of 1000 Hz). A medium can pass frequencies from 3000 to 4000 Hz (a bandwidth of 1000 Hz). Can this signal faithfully pass through this medium? Solution: The answer is definitely no. Although the signal can have the same bandwidth (1000 Hz), the range does not overlap. The medium can only pass the frequencies between 3000 and 4000 Hz; the signal is totally lost.

Digital Signals 3. Digital Signals In addition to being represented by an analog signal, information can also be represented by a digital signal. For example, a 1 can be encoded as a positive voltage and a 0 as zero voltage.

Digital Signals 3.1. Bit Rate and Bit Interval • Bit Rate Most digital signals are non-periodic, and thus period and frequency are not appropriate characteristics. Another term-bit rate (instead of frequency) is used to describe digital signals. The bit rate is the number of bits sent in 1 second, expressed in bits per second (bps).

Digital Signals Example: Assume we need to download text documents at the rate of 100 pages per second. What is the required bit rate of the channel? Assume that a page is an average of 24 lines with 80 characters in each line and one character requires 8 bits. Solution

Digital Signals Solution A page is an average of 24 lines with 80 characters in each line. If we assume that one character requires 8 bits, the bit rate is 100 x 24 x 80 x 8 =1,536,000 bps =1.536 Mbps

Digital Signals • Bit Interval Bit Interval is a duration (expressed in second) of one bit. It is the inverse of bit rate. Bit Interval = 1/Bit rate Example: A digital signal has bit rate 2000 bps. What is its bit interval? Solution: bit interval = 1/bit rate = 1/2000 s = 0.0005s = 500 µs 1 s = 8 bit intervals Bit Interval

Digital Signals 3.2. Transmission of Digital Signals A computer network is designed to send information from one point to another. This information needs to be converted to either a digital signal or an analog signal for transmission. In digital transmission, the required bandwidth is proportional (~) to the bit rate; if we need to send bits faster, we need more bandwidth.

Data Communications and Networking