Digital Signal Introduction PDF

UNIT II 2. Introduction to Physical layer 3. Introduction to the Data Link Layer 4. Wireless LANs 2. Introduction to Physical layer  INTRODUCTION TO PHYSICAL LAYER One of the major functions of the physical layer is to move data in the form of electromagnetic signals across a transmi...

UNIT II 2. Introduction to Physical layer 3. Introduction to the Data Link Layer 4. Wireless LANs 2. Introduction to Physical layer  INTRODUCTION TO PHYSICAL LAYER 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. For example, a photograph must first be changed to a form that transmission media can accept. Transmission media work by conducting energy along a physical path. For transmission, data needs to be changed to signals. NIKITA MADWAL  ANALOG AND DIGITAL DATA To be transmitted, data must be transformed to electromagnetic signals. Data can be Analog or Digital. 1. Analog data refers to information that is continuous; ex. An analog clock that has hour, minute, and second hands gives information in a continuous form; the movements of the hands are continuous , sounds made by a human voice 2. Digital data refers to information that has discrete states. Digital data take on discrete values. ex. A digital clock that reports the hours and the minutes will change suddenly from 8:05 to 8:06.,data are stored in computer memory in the form of 0s and 1s NIKITA MADWAL  SIGNALS Signals can be of two types: 1. Analog Signal: They have infinite number of values in a range. 2. Digital Signal: They have limited number of defined values NIKITA MADWAL  PERIODIC & NON PERIODIC SIGNALS Signals which repeat itself after a fixed time period are called Periodic Signals. A periodic signal completes a pattern within a measurable time frame, called a period, and repeats that pattern over subsequent identical periods. The completion of one full pattern is called a cycle. A non-periodic signal changes without exhibiting a pattern or cycle that repeats over time. Signals which do not repeat itself after a fixed time period are called Non-Periodic Signals. In data communications, we commonly use periodic analog signals and non- periodic digital signals. NIKITA MADWAL PERIODIC ANALOG SIGNALS Periodic analog signals can be classified as simple or composite. 1. A simple periodic analog signal, a sine wave, cannot be decomposed into simpler signals. 2. A composite periodic analog signal is composed of multiple sine waves. NIKITA MADWAL ❖1. Sine Wave A sine wave can be represented by three parameters: peak amplitude frequency phase NIKITA MADWAL  A. Peak Amplitude The peak amplitude of a signal is the absolute value of the highest intensity. For electric signals, peak amplitude is normally measured in volts. NIKITA MADWAL  B. Period and Frequency Frequency refers to the number of cycles completed by the wave in one second. Frequency is formally expressed in Hertz (Hz), which is cycle per second. Period refers to the time taken by the wave to complete one cycle. Period is formally expressed in seconds. NIKITA MADWAL  Frequency Example: If a wave completes 10 cycles in 1 second, its frequency is 10 Hz. Period Example: If it takes 0.1 seconds for one complete cycle of the wave, then the period is 0.1 seconds. NIKITA MADWAL  Two signals with the same amplitude and phase, but different frequencies NIKITA MADWAL NIKITA MADWAL  Example 3.3 The power we use at home has a frequency of 60Hz. The period of this sine wave can be determined as follows: NIKITA MADWAL  Solve Calculate the period of a wave whose frequency is 50 Hz NIKITA MADWAL  Solve Calculate the frequency of a wave whose time period is 0.002 s NIKITA MADWAL  Example 3.4 Express a period of 100 ms in microseconds. NIKITA MADWAL  Example 3.5 The period of a signal is 100 ms. What is its frequency in kilohertz? NIKITA MADWAL  Solve The period of a signal is 100 ms. What is its frequency in megahertz? NIKITA MADWAL NIKITA MADWAL  C. Phase Phase describes the position of the waveform with respect to time (specifically 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. Phase is measured in degrees or radians [360º is 2π rad; 1º is 2π/360 rad, and 1 rad is 360/(2π)]. A phase shift of 360º corresponds to a shift of a complete period; a phase shift of 180° corresponds to a shift of one-half of a period; and a phase shift of 90º corresponds to a shift of one-quarter of a period NIKITA MADWAL NIKITA MADWAL NIKITA MADWAL  Looking at Figure 3.6, we can say that a. A sine wave with a phase of 0° starts at time 0 with a zero amplitude. The amplitude is increasing. b. A sine wave with a phase of 90° starts at time 0 with a peak amplitude. The amplitude is decreasing. c. 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 a. A sine wave with a phase of 0° is not shifted. b. A sine wave with a phase of 90° is shifted to the left by cycle. c. A sine wave with a phase of 180° is shifted to the left by cycle. NIKITA MADWAL  Example 3.6 1 A sine wave is offset cycle with respect to time 0. What is its phase in 6 degrees and radians? NIKITA MADWAL ❖Wavelength The wavelength of a signal refers to the relationship between frequency (or period) and propagation speed of the wave through a medium. The wavelength is the distance a signal travels in one period. It is given by Wavelength = Propagation Speed * Period OR Wavelength =Propagation Speed / Frequency NIKITA MADWAL  It is represented by the symbol : λ (pronounced as lamda) It is measured in micrometers. Wavelength depends on both the frequency and the medium NIKITA MADWAL ❖Time and Frequency Domain A sine wave can be represented either in the time domain or frequency domain. The time-domain plot shows changes in signal amplitude with respect to time. It indicates time and amplitude relation of a signal. The frequency-domain plot shows the relationship between signal frequency and peak amplitude. NIKITA MADWAL NIKITA MADWAL  The frequency domain is easy to plot and conveys the information that one can find in a time domain plot. The advantage of the frequency domain is that we can immediately see the values of the frequency and peak amplitude. A complete sine wave in the time domain is represented by one spike in frequency domain. The figure below show time and frequency domain plots of three sine waves. NIKITA MADWAL ❖2. Composite Single A composite signal is a combination of two or more simple sine waves with different frequency, phase and amplitude. According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies; If the composite signal is non-periodic, the decomposition gives combination of sine waves with continuous frequencies. 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 NIKITA MADWAL NIKITA MADWAL NIKITA MADWAL ❖Bandwidth The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal. NIKITA MADWAL  Example 3.10 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 NIKITA MADWAL  Example 3.11 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. NIKITA MADWAL  Example 3.12 A nonperiodic composite signal has a bandwidth of 200 kHz, with a middle frequency of 140 kHz and peak amplitude of 20 V. The two extreme frequencies have an amplitude of 0. Draw the frequency domain of the signal. NIKITA MADWAL NIKITA MADWAL  Digital Signal A digital is a signal that has discrete values. The signal will have value that is not continuous. NIKITA MADWAL NIKITA MADWAL  Relation between levels of signal and bit rate Example 3.16 A digital signal has eight levels. How many bits are needed per level? Example 3.17 A digital signal has nine levels. How many bits are needed per level? Each signal level is represented by 3.17 bits. However, this answer is not realistic. The number of bits sent per level needs to be an integer as well as a power of 2. For this example, 4 bits can represent one level. NIKITA MADWAL  Relation between levels of signal and bit rate Example 3.16 A digital signal has eight levels. How many bits are needed per level? Example 3.17 A digital signal has nine levels. How many bits are needed per level? Each signal level is represented by 3.17 bits. However, this answer is not realistic. The number of bits sent per level needs to be an integer as well as a power of 2. For this example, 4 bits can represent one level. NIKITA MADWAL ❖Bit Rate It is the number of bits transmitted in one second. It is expressed as bits per second (bps). Relation between bit rate and bit interval can be as follows Bit rate = 1 / Bit interval Note: similar to the frequency for Analog NIKITA MADWAL ❖Bit Length The bit length is the distance one bit occupies on the transmission medium. Bit Length= Propagation speed * bit duration Note: Similar to wavelength for Analog. NIKITA MADWAL ❖Transmission of digital signals We can transmit a digital signal by using one of two different approaches: 1.Baseband transmission or 2.Broadband transmission(using modulation). NIKITA MADWAL  From the point of view of transmission, there are two types of channels: 1. Low pass Channel This channel has the lowest frequency as ‘0‘ and highest frequency as some non-zero frequency ‘f1‘. This channel can pass all the frequencies in the range 0 to f1. 2.Band pass channel This channel has the lowest frequency as some non-zero frequency ‘f1‘ and highest frequency as some non-zero frequency ‘f2‘. This channel can pass all the frequencies in the range f1 to f2. NIKITA MADWAL NIKITA MADWAL  1.Baseband transmission Baseband transmission means sending a digital signal over a channel without changing the digital signal to an analog signal. Baseband transmission requires a low-pass channel. In baseband transmission, the bandwidth of the signal to be transmitted has to be less than the bandwidth of the channel. NIKITA MADWAL  Ex. Consider a Baseband channel with lower frequency 0Hz and higher frequency 100Hz, hence its bandwidth is 100 (Bandwidth is calculated by getting the difference between the highest and lowest frequency). We can easily transmit a signal with frequency below 100Hz, such a channel whose bandwidth is more than the bandwidth of the signal is called Wideband channel Logically a signal with frequency say 120Hz will be blocked resulting in loss of information, such a channel whose bandwidth is less than the bandwidth of the signal is called Narrowband channel NIKITA MADWAL  2. Broadband transmission Broadband transmission or modulation means changing the digital signal to an analog signal for transmission. Modulation allows us to use a bandpass channel-a channel with a bandwidth that does not start from zero. If the available channel is a bandpass channel, we cannot send the digital signal directly to the channel; we need to convert the digital signal to an analog signal before transmission NIKITA MADWAL NIKITA MADWAL