Chương 1: CÁC KHÁI NIỆM CƠ BẢN 1.5 Môi trường truyền 1. Môi trường có định hướng 1. Môi trường không định hướng 4 1.1 Dữ liệu và tín hiệu 1. Dữ liệu số To be transmitted, data must be transformed to electromagnetic signals Data can be analog or digital.
The term analog data refers to information that is continuous; digital data refers to information that has discrete states. Analog data take on continuous values. Digital data take on discrete values.1 Dữ liệu và tín hiệu 1. Tín hiệu tương tự và số Signals can be analog or digital.
Analog signals can have an infinite number of values in a range; digital signals can have only a limited number of values.1 Dữ liệu và tín hiệu 1.3 Tín hiệu chu kỳ và không chu kỳ In data communications, we commonly use periodic analog signals and nonperiodic digital signals. a) 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.1 Dữ liệu và tín hiệu Figure 3.2 A sine wave Example 3.1 The power in your house can be represented by a sine wave with a peak amplitude of 155 to 170 V.
However, it is common knowledge that the voltage of the power in U. homes is 110 to 120 V. This discrepancy is due to the fact that these are root mean square (rms) values. The signal is squared and then the average 8 amplitude is calculated.
The peak value is equal to 2 × rms value.1 Dữ liệu và tín hiệu Figure 3.3 Two signals with the same phase and frequency, but different amplitudes 9 1.1 Dữ liệu và tín hiệu Frequency and period are the inverse of each other.1 Dữ liệu và tín hiệu Figure 3.4 Two signals with the same amplitude and phase, but different frequencies 11 1.1 Dữ liệu và tín hiệu Example 3.3 The power we use at home has a frequency of 60 Hz. The period of this sine wave can be determined as follows: 12 1.1 Dữ liệu và tín hiệu Example 3.5 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).1 Dữ liệu và tín hiệu Figure 3.7 The time-domain and frequency-domain plots of a sine wave 14 1.1 Dữ liệu và tín hiệu 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. According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases.1 Dữ liệu và tín hiệu 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.1 Dữ liệu và tín hiệu Example 3.9 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.1 Dữ liệu và tín hiệu Figure 3.9 A composite periodic signal 18 1.1 Dữ liệu và tín hiệu Figure 3.10 Decomposition of a composite periodic signal in the time and frequency domains 19 1.1 Dữ liệu và tín hiệu Example 3.11 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.1 Dữ liệu và tín hiệu Figure 3.11 The time and frequency domains of a nonperiodic signal 21 1.1 Dữ liệu và tín hiệu The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal.1 Dữ liệu và tín hiệu Figure 3.12 The bandwidth of periodic and nonperiodic composite signals 23 1.1 Dữ liệu và tín hiệu 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. Solution Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then The spectrum has only five spikes, at 100, 300, 500, 700, and 900 Hz (see Figure 3.1 Dữ liệu và tín hiệu Figure 3.13 The bandwidth for Example 3.1 Dữ liệu và tín hiệu 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. Solution The lowest frequency must be at 40 kHz and the highest at 240 kHz.15 shows the frequency domain and the bandwidth.1 Dữ liệu và tín hiệu Figure 3.15 The bandwidth for Example 3.1 Dữ liệu và tín hiệu b) 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. A digital signal can have more than two levels.
In this case, we can send more than 1 bit for each level.1 Dữ liệu và tín hiệu Figure 3.16 Two digital signals: one with two signal levels and the other with four signal levels 29 1.1 Dữ liệu và tín hiệu Example 3.16 A digital signal has eight levels. How many bits are needed per level? We calculate the number of bits from the formula Each signal level is represented by 3 bits.1 Dữ liệu và tín hiệu Example 3.19 A digitized voice channel, as we will see in Chapter 4, is made by digitizing a 4-kHz bandwidth analog voice signal. We need to sample the signal at twice the highest frequency (two samples per hertz). We assume that each sample requires 8 bits.
What is the required bit rate? Solution The bit rate can be calculated as 31 1.1 Dữ liệu và tín hiệu Figure 3.1 Dữ liệu và tín hiệu A digital signal is a composite analog signal with an infinite bandwidth.1 Dữ liệu và tín hiệu Figure 3.19 Bandwidths of two low-pass channels 34 1.1 Dữ liệu và tín hiệu Figure 3.20 Baseband transmission using a dedicated medium Baseband transmission of a digital signal that preserves the shape of the digital signal is possible only if we have a low-pass channel with an infinite or very wide bandwidth.1 Dữ liệu và tín hiệu 1.6 Nhiễu trong môi trường truyền Signals travel through transmission media, which are not perfect. The imperfection causes signal impairment. This means that the signal at the beginning of the medium is not the same as the signal at the end of the medium. What is sent is not what is received.
Three causes of impairment are attenuation, distortion, and noise.1 Dữ liệu và tín hiệu Figure 3.25 Causes of impairment 37 1.1 Dữ liệu và tín hiệu Figure 3.1 Dữ liệu và tín hiệu Suppose a signal travels through a transmission medium and its power is reduced to one-half. This means that P2 is (1/2)P1. In this case, the attenuation (loss of power) can be calculated as A loss of 3 dB (–3 dB) is equivalent to losing one-half the power.1 Dữ liệu và tín hiệu One reason that engineers use the decibel to measure the changes in the strength of a signal is that decibel numbers can be added (or subtracted) when we are measuring several points (cascading) instead of just two.27 a signal travels from point 1 to point 4. In this case, the decibel value can be calculated as 40 1.1 Dữ liệu và tín hiệu Figure 3.27 Decibels for Example 3.1 Dữ liệu và tín hiệu Figure 3.1 Dữ liệu và tín hiệu Figure 3.1 Dữ liệu và tín hiệu The power of a signal is 10 mW and the power of the noise is 1 μW; what are the values of SNR and SNRdB ? Solution The values of SNR and SNRdB can be calculated as follows: 44 1.1 Dữ liệu và tín hiệu Example 3.32 The values of SNR and SNRdB for a noiseless channel are We can never achieve this ratio in real life; it is an ideal.1 Dữ liệu và tín hiệu Figure 3.30 Two cases of SNR: a high SNR and a low SNR 46 1.1 Dữ liệu và tín hiệu DATA RATE LIMITS A very important consideration in data communications is how fast we can send data, in bits per second, over a channel.
Data rate depends on three factors: 1. The bandwidth available 2. The level of the signals we use 3. The quality of the channel (the level of noise) 47 1.1 Dữ liệu và tín hiệu Example 3.34 Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels.
The maximum bit rate can be calculated as 48 1.1 Dữ liệu và tín hiệu Example 3.37 Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zero. In other words, the noise is so strong that the signal is faint. For this channel the capacity C is calculated as This means that the capacity of this channel is zero regardless of the bandwidth. In other words, we cannot receive any data through this channel.1 Dữ liệu và tín hiệu Example 3.38 We can calculate the theoretical highest bit rate of a regular telephone line.
A telephone line normally has a bandwidth of 3000. The signal-to-noise ratio is usually 3162. For this channel the capacity is calculated as This means that the highest bit rate for a telephone line is 34. If we want to send data faster than this, we can either increase the bandwidth of the line or improve the signal-to-noise ratio.