CHAPTER 3 DATA AND SIGNAL 9/20/2018 ITT 300

Position of The Physical Layer 9/20/2018 ITT 300

Duties of Physical Layer Bit-signal transformation Bit-rate control Bit synchronization Bandwidth utilization: Multiplexing 9/20/2018 ITT 300

Data & Signal Data Entities that convey meaning To be transmitted, data must be transformed to electromagnetic signals. Signal Electric or electromagnetic representations of data means by which data are propagated Transmission Communication of data by propagation and processing of signals 9/20/2018 ITT 300

Analog and Digital Data Analog data refers to information that is continuous e.g human voice, video Analog Data Digital refers to information that has discrete states e.g. data stored in the memory of computer in the form of 0s and 1s Digital Data 9/20/2018 ITT 300

Analog and Digital Signals can have an infinite number of values in a range Analog signals can have only a limited number of values Digital signals The simplest way to show signals is by plotting them on a pair of perpendicular axes: -vertical axis represents the value or strength of a signal -horizontal axis represents time 9/20/2018 ITT 300

Comparison of Analog and Digital Signal 9/20/2018 ITT 300

Periodic and Nonperiodic Signals Both analog and digital signals can be in two forms; In data communications, we commonly use periodic analog signals and nonperiodic digital signals Periodic signals consists of continuous repetitive pattern within a time frame called period the completion of one full pattern is called cycle Nonperiodic signals (aperiodic) has no repetitive pattern can be decomposed into infinite number of periodic signals 9/20/2018 ITT 300

Periodic Signals 9/20/2018 ITT 300

Nonperiodic Signals 9/20/2018 ITT 300

Periodic Analog Signals Can be classified as simple or composite A simple periodic analog signal: a sine wave, cannot be decomposed into simpler signals A composite periodic analog signal: is composed of multiple sine waves Sine wave can be described by three characteristics: Peak amplitude (A) Frequency (f) Phase (ø) 9/20/2018 ITT 300

Sine Wave Signal S(t) = A sin (2  f t +  ) 9/20/2018 ITT 300

Sine Wave: Peak amplitude (A) The value of its highest intensity, proportional to the energy it carries Measured by volts 9/20/2018 ITT 300

Sine Wave: Peak amplitude (A) Two signals with the same phase and frequency, but different amplitudes 9/20/2018 ITT 300

Sine Wave: Frequency ( f ) Period (T) and frequency (f) The amount of time (in seconds) needs to complete in one cycle Period = time for one repetition (T) Frequency (f) = the number of period in a second (expressed in Hertz) Frequency and period are the inverse of each other T= 1 and f = 1 f T 9/20/2018 ITT 300

Sine Wave: Frequency ( f ) Two signals with the same amplitude and phase, but different frequencies 9/20/2018 ITT 300

Sine Wave: Frequency ( f ) Frequency is the rate of change with respect to time. high frequency = change in a short span of time low frequency = change over a long span of time zero frequency = if a signal does not change at all infinite frequency= if a signal changes instantaneously 9/20/2018 ITT 300

Units of Period and Frequency 9/20/2018 ITT 300

Example 1: Express a period of 100 ms in microseconds. Solution We make the following substitutions: 100 ms = 100  10-3 s = 102  10-3  106 μs = 105 μs 1 ms = 10-3 s 1 s = 106 μs 9/20/2018 ITT 300

Example 2: A period of signals is100 ms. Express the corresponding frequency in kilohertz. Solution First we change 100 ms to seconds 100 ms = 100  10-3 s = 102  10-3 s = 10-1 s Then we calculate the frequency from the period f = 1 Hz = 10 Hz = 10 x 10-3 kHz = 10-2 kHz 10-1 T= 1 and f = 1 f T 1 ms = 10-3 s 1 Hz = 10-3 kHz 9/20/2018 ITT 300

Example 3: Express a period of 1,000,000 μs in second. Solution 9/20/2018 ITT 300

Example 4: A period of signals is 1,000,000 μs. Express the corresponding frequency in kilohertz. Solution 9/20/2018 ITT 300

Example 5: The power in your house (North America) can be represented by a sine wave with a peak amplitude between 110 to 220 V. The power we use at home (North America) has a frequency of 60 Hz. What is the period of this sine wave? Solution T = 1 = 1 = 0.0166 s = 0.0166 x 10-3 ms = 16.6 ms f 60 9/20/2018 ITT 300

Example 6: The power in your house (Malaysia) can be represented by a sine wave with a peak amplitude between 220 to 240 V. The power we use at home has a frequency of 50 Hz. What is the period of this sine wave? Solution 9/20/2018 ITT 300

Sine Wave : Phase (ø) Phase (ø) Described the position of the waveform relative to time zero Measured in degrees or radians: 360° = 2π rad 1° = 2π/360 rad 1 rad = 360/(2π) Four types of phase: 0° 90° 180° 270° 9/20/2018 ITT 300

Sine Wave : Phase (ø) Phase change 9/20/2018 ITT 300

Sine Wave : Phase (ø) Four sine waves with the same amplitude and frequency, but different phases 9/20/2018 ITT 300

Example 7: A sine wave is offset 1/6 of a cycle with respect to time 0. What is its phase in degrees and radians? Solution 1) Phase in degree: One complete cycle is 360 degrees. Therefore, 1/6 cycle: 2) Phase in radians: 1° is 2π/360 rad. Therefore, 60° : 1 x 360 = 60° 6 60 ° x 2π rad = π = 1.046 rad 360 3 9/20/2018 ITT 300

Example 8: A sine wave is offset 1/8 cycle with respect to time 0. What is its phase in degrees and radians? Solution 1) Phase in degree: 2) Phase in radians: 9/20/2018 ITT 300

Example 9: A sine wave is offset 3/4 cycle with respect to time 0. What is its phase in degrees and radians? Solution 1) Phase in degree: 2) Phase in radians: 9/20/2018 ITT 300

Sine Wave: Wavelength Distance occupied by one cycle Distance between two points of corresponding phase in two consecutive cycles It binds the period of a sine wave to the propagation speed of the medium 9/20/2018 ITT 300

Wavelength= propagation speed x period= propagation speed Sine Wave: Wavelength Wavelength can be calculated if one is given the propagation speed (the speed of light) and the period of the signal. However, since period and frequency are related to each other, if we represent: wavelength = λ micrometers or microns propagation speed = c frequency = f c = 3*108 m/s Wavelength= propagation speed x period= propagation speed frequency λ = ct or λ = c d f 9/20/2018 ITT 300

Example 10: λ = c = 3*108 8= 0.75 * 10-6 m = 0.75 microns Calculate the wavelength of red light if its frequency is 4 x 1014 Solution λ = c d f λ = c = 3*108 8= 0.75 * 10-6 m = 0.75 microns f 4 x 1014 9/20/2018 ITT 300

Sine Wave: Time & Frequency Domain Time and Frequency domain The time-domain plot shows changes in signal amplitude with respect to time To show relationship between amplitude and frequency, we use frequency domain plot An analog signal is best represented in the frequency domain 9/20/2018 ITT 300

Sine Wave: Time & Frequency Domain Time and frequency domains 9/20/2018 ITT 300

Sine Wave: Time & Frequency Domain The frequency domain is more compact and useful when we are dealing with more than one sine wave. e.g: Figure below shows three sine waves, each with different amplitude and frequency. All can be represented by three frequency spikes in the frequency domain. 9/20/2018 ITT 300

Composite Signals A single-frequency sine wave is NOT useful in data communications; We need to send a composite signal, a signal made of many simple sine waves. Fourier analysis any combination of simple sine waves with different frequencies, amplitudes, and phases. 9/20/2018 ITT 300

Composite Signals If the composite signal is periodic: the decomposition gives a series of signals with discrete frequencies If the composite signal is nonperiodic: the decomposition gives a combination of sine waves with continuous frequencies 9/20/2018 ITT 300

Composite Signals Example: Figure below shows a periodic composite signal with frequency ( f ). This type of signal is not typical of those found in data communications. We can consider it to be three alarm systems, each with a different frequency. The analysis of this signal can give us a good understanding of how to decompose signals. 9/20/2018 ITT 300

A composite periodic signal Composite Signals A composite periodic signal 9/20/2018 ITT 300

Decomposition of a composite periodic signal in the time and Composite Signals Decomposition of a composite periodic signal in the time and frequency domains 9/20/2018 ITT 300

Composite Signals Example: Figure below shows a nonperiodic composite signal. It can be the signal created by a microphone or a telephone set when a word or two is pronounced. In this case, the composite signal cannot be periodic, because that implies that we are repeating the same word or words with exactly the same tone. 9/20/2018 ITT 300

The time and frequency domains of a nonperiodic signal Composite Signals The time and frequency domains of a nonperiodic signal 9/20/2018 ITT 300

Bandwidth (B) The bandwidth of a composite signal is the difference between the highest (fh) and the lowest (fl) frequencies contained in that signal. The bandwidth of a medium: the difference between the highest (fh) and the lowest (fl) frequencies that the medium can satisfactorily pass B = fh - fl 9/20/2018 ITT 300

Bandwidth (B) Bandwidth 9/20/2018 ITT 300

Example 10: If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is the bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V. Solution Bandwidth: B = fh - fl = 900 - 100 = 800 Hz The spectrum has only five spikes, at 100, 300, 500, 700, and 900 (see Figure 3.9 ) 9/20/2018 ITT 300

The bandwidth for Example 10 Bandwidth spectrum: The spectrum has only five spikes, at 100, 300, 500, 700, and 900. The bandwidth for Example 10 9/20/2018 ITT 300

Example 11: A 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 integral frequencies of the same amplitude. Solution 9/20/2018 ITT 300

Example 11: Bandwidth spectrum: The spectrum has only five spikes, at 100, 300, 500, 700, and 900. 9/20/2018 ITT 300

Example 12: 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 9/20/2018 ITT 300

Exercises Given the frequencies listed below, calculate the corresponding periods. 8 MHz 140KHz Given the following periods, calculate the corresponding frequencies. 5 s 220 ns What is the phase shift for the following? a. A sine wave with the maximum amplitude at time zero b. A sine wave with maximum amplitude after 1/4 cycle 9/20/2018 ITT 300

Exercises What is the bandwidth of a signal that can be decomposed into five sine waves with frequencies at 0, 20, 50, 100, and 200 Hz? All peak amplitudes are the same. Draw the bandwidth. A periodic composite signal with a bandwidth of 2000Hz is composed of two sine waves. The first one has a frequency of 100 Hz with a maximum amplitude of 20 V; the second one has a maximum amplitude of 5 V. Draw the bandwidth. Which signal has a wider bandwidth, a sine wave with a frequency of I 00 Hz or a sine wave with a frequency of 200 Hz? 9/20/2018 ITT 300