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An electrical communication system enclosed in the dashed box employs electrical signals to deliver user information voice, audio, video, data from source to destination(s). An input transducer may be required if the source information is not represented by an electrical signal. For example, in your cell phone, a microphone is used as input transducer that converts speech (sound) to electrical voice signal which is the input electrical signal to the electrical communication system. Correspondingly, on the receiving side, after the electrical signal of the same format as the input electrical signal is extracted by the receiver, the output transducer (such as a speaker) converts the signal to the format suitable for the destination user or destination device. 2
The transmitter is responsible for converting the input electrical signal to a transmitted signal, an electrical signal suitable for propagating through the channel to be used to deliver the signal. For example, if the channel is a fiber optic link, the transmitted signal has to be optical (a special form of electrical signal) which entails a laser in the transmitter. If the channel is a wireless link, then the signal is typically a radio signal (another special form of electrical signal also known as electromagnetic wave) which requires a radio transmitter and an antenna in the transmitter block. Some key functions implemented in the transmitter are modulation, filtering, encoding, and signal transmitting (to be elaborated) On the receiving end of the communication system, the received signal is a weakened and possibly distorted version of the transmitted signal plus interference and noise. The receiver is responsible for removing as much as possible noise, interference, and distortion, and then for converting the signal back to the same electrical signal format as the input electrical signal. Some key functions implemented in the receiver are filtering, amplification, demodulation, decoding (to be elaborated) Remark: a channel may be shared by many simultaneous communications 3
A communication signal can be represented and displayed as a function of time, called signal waveform. Generally functions of time are not limited to signals within a communication system. There are a lot of functions of time encountered in real life: stock market index versus time, Evanston s temperature versus time, your weight versus time, a patient s pulses versus time, to name a few. There are two distinctive kinds of waveforms: analog waveform and digital waveform. Examples of analog waveform are those generated form voice, audio, and video. Examples of digital waveform are those generated form computer data and digitized voice/audio/video. 4
The most basic electrical signal is the sine wave, also called sinusoid. The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. (Wikipedia) Shown in the slide is the waveform of a sine wave. Mathematically, it is a periodic function (i.e., it repeats after every period ) characterized by three parameters: amplitude, frequency, and phase. Phase is meaningful only when there are more than one sine wave involved. Amplitude indicates the peak value of the waveform, which represents the strength of the sine wave. Frequency stands for the oscillation rate (i.e., rate of moving up and down) of the waveform; it is equal to 1/T, T being the period. This is because: if the waveform repeats itself every T seconds, then it oscillates 1/T times per second. For instance, a 100-Hz sine wave oscillates 100 times per second, as it repeats every 1/100 of one second. Any communication signal is made up of sine waves of varying frequencies. 5
A familiar sine wave in practice: household 110-Volt AC voltage is a sine wave with an amplitude of 156 Volts and a frequency of 60-Hz 6
This slide is an illustration of two sine waves with different amplitudes and frequencies. Two sine waves are displayed on the same graph here, where the taller (thus stronger) sine wave has a lower frequency (i.e., it oscillates at a slower rate than the other sine wave), the other sine wave has a smaller amplitude but a higher frequency. 7
This slides shows an illustrative example of three sinusoids with the same amplitude, the same frequency, but different timings. All three sinusoids have the same strength (same amplitude), the same oscillation rate (the same frequency), but they are off in timing; that is, they are generated at different times. Note from high school math: the sine function takes angle as its argument, and is a periodic function with period 2 (radians) or 360 degrees. Therefore the timing difference between two sinusoids is quantified by an angle, called phase inside the sine function. Naturally, the value of the phase is between 0 and 2. In communication systems, we customarily define the range of the phase as from - and + instead. When there are multiple sinusoids present, their phases become important. In this example, the three sinusoids of equal strength add up to ZERO, that is, they cancel out completely. (This is an extreme example used to illustrate the importance of phase.) Multiple-path Fading: When multiple versions of the same radio wave carrying your cell phone signal arrive at the base station due to ground and building reflections, they are of different amplitudes and phases. This is known as multiple-path effect, which does not strengthen your signal s reception. On the contrary, it weakens it. 8
When all three parameters of a sine wave are included, the mathematical expression for a general sine wave is s(t) = A sin (2 f 0 t + ) The strength of a sine wave can also be expressed in terms of signal power P, which is related to amplitude A by P = A 2 /2. While the unit for amplitude is Volt (or V in short), the unit for power is Watt (or W in short). Note that the frequency and the phase of a sine wave have nothing to do with the power of the sine wave. Why are sine waves important for communication systems? 1. They are the fundamental components ( genes ) of any signal, analog or digital: voice, audio, video, data, Note: a single sine wave component of a signal is often referred to, simply, as a frequency component 2. They are used as carriers in most wired communication channels and all wireless communication channels for transmission of information-bearing signals 9
The key parameter of a sine wave that distinguishes it from other sine waves is its frequency. When a signal is decomposed into multiple sine waves of different frequencies, it can be displayed as a function of frequency called signal spectrum. For example, in this slide, a single sine wave with amplitude 5 Volt, frequency 4000 Hz and phase -160 is displayed in the frequency domain, i.e., as a function of frequency. There are two things to display versus the frequency: amplitude and phase. The display of the signal s amplitude against its frequency is called amplitude spectrum. The display of the signal s phase against its frequency is called phase spectrum. With an amplitude of 5 Volt, the power of the signal is 12.5 Watt. The display of the signal s power against it frequency is called power spectrum. In this simple example, each spectrum is a function of time with a single point because there is only one sine wave and thus one single frequency. We shall focus primarily on the amplitude spectrum when dealing with frequencydomain representation of a signal. Here an amplitude of 5 Volt is found in the signal at frequency 4000 Hz. Thus the amplitude spectrum in this example is simply a function of frequency with a single point (commonly displayed as a bar) at f=4000 Hz. 10
It may be hard to appreciate the usefulness of signal spectrum when there is only one single sine wave In this slide, a signal consisting of two sine waves is illustrated in the frequency domain, one of them has an amplitude A and frequency f A, the other B and f B. The amplitude spectrum now consists of two bars, one has an amplitude value A at frequency f A, the other has an amplitude value B at frequency f B. 11
Extending to a signal x(t) that is made up of three sine waves The amplitude spectrum now contains three bars located at frequencies 1000, 2000, and 4000 Hz, respectively. These bars will be referred to as spectral lines. The phase spectrum of the signal is also displayed and it also contains three bars, although one of the bars has a zero value (so the bar collapses to a dot ) in this case. 12
More generally, Fourier Theory asserts that any signal waveform (or any function of time), whether it is analog or digital, can be decomposed into sine waves of differing frequencies. The set of frequencies of the sine waves that make up this signal typically spans a range. The size of this frequency range is called the bandwidth of the signal, or signal bandwidth. When all the spectral lines (bars) are displayed within the bandwidth, they illuminates a shaped area in the frequency-domain plot. This outline of this shape is a function of frequency called the (continuous) signal spectrum. In the slide, A(f) and D(f) denote the amplitude spectra of the two waveforms. Both are functions of frequency. Shown on the right of this slides are examples of amplitude spectrum. The shapes of the spectra are not so important and have been drawn arbitrarily, while the frequency range and the bandwidth defined by the signal spectrum is the most informative. Almost all the original forms of information signals (voice, audio, video, baseband data) have a frequency range in the low frequency area. For example, voice has a frequency range: 200-3200 Hz, commercial broadcast AM audio: 0-5 khz, analog video: 0-6 MHz, and baseband data signal: 0-B Hz, where B is proportional to data rate (will be elaborated in a later chapter) Note: A spectrum analyzer is a device used to display the spectrum of a signal. 13
When a signal passes through a communication channel or an electronic device (e.g., an amplifier), the signal spectrum is filtered by the channel or device. Specifically, a communication channel/device does not treat all the sine waves that make up the signal equally. For convenience, in the sequel, filter will be used to represent any communication device. Mathematically, the frequency-selective behavior of the channel/filter is represented as a function of frequency (just like the amplitude spectrum of the signal) called frequency response. If a signal with amplitude spectrum X(f) is passed through a channel/filter with frequency response H(f), then the output of the channel/filter will be a signal with amplitude spectrum Y(f) = H(f) X(f) multiplication of two functions of frequency Filtering Effect: if H(f 1 ) = 0, then Y(f 1 ) = 0, no matter what X(f 1 ) is. That is, the sine wave component with frequency f 1 is removed when the channel or filter has a zero response at frequency f 1. If H(f 2 ) = 1, then Y(f 2 ) = X(f 2 ), that is, the sine wave component with frequency f 1 is passed without change. If H(f 3 ) = 0.000001, then Y(f 3 ) = 0.000001 X(f 3 ), that is, the magnitude of the sine wave component with frequency f 3 is scaled by 1000000. Essentially, H(f) serves as amplitude multiplier for input sine wave with frequency f. 14
The frequency response of a filter generally consists of three sub-ranges of frequencies: the passband, the stopband, and the transition band. Within the passband, the frequency response is at or near the peak; within the stopband, the frequency response is nearly zero; and within the transition band, the frequency response varies largely from high to low. Frequency components of the signal within the passband will pass through the channel/filter without significant losses; frequency components of the signal within the stopband will be removed almost entirely; frequency components of the signal within the transition band will be subject to distortion since they are multiplied by largely varying frequency responses. It is desired to fit the signal of interest inside the passband of the channel or of the filter such that the frequency components of the signal will not be subject to significant suppression. The width of the passband is thus called the channel bandwidth or filter bandwidth. A quality filter should have a nearly flat frequency response within its passband and a narrow transition band. 15
When a signal travels through any communication medium, wired or wireless, its strength declines as distance increases a phenomenon known as power attenuation. Over a communication channel or a filter, the ratio of the input power to the output power is defined as power loss. For example, if a signal is transmitted using 10 Watt of power, and its strength is reduced to 1 Watt at reception, the power loss introduced by the channel is L = 10W/1W = 10. The power gain is defined as G = 1/L. That is, a power loss of 10 amounts to a power gain of 1/10. A power amplifier has power gain larger than 1 and a power loss smaller than 1. In communication systems, power loss and power gain are commonly expressed in decibels (db). L and G can be converted to decibels by taking the log and then multiplied by 10. As a result, L = 100 = 20 db L = 100000 = 50 db L = 1 = 0 db (no loss) L = 2 = 3 db (power is halved) 16
The following refers to the right column of Slide 16: In any wired medium twisted pair copper wires, optical fiber, coax cables power loss L increases with distance exponentially. As a result, in decibels, the power loss L db increases linearly with distance. Thus for wired media, power loss in decibels greatly ease the computation when the distance increases or decreases. Power loss rating is thus expressed in terms of attenuation coefficient (e.g., in db/meter, db/30ft, db/km, etc.) for wired media. In a line-of-sight wireless medium, power loss L increases with distance squared. (Note: the loss in decibels does not help in computing power losses when the distance increases or decreases.) In an urban environment, the power loss through a wireless medium without line-of-sight increases with distance raised to the power of k, where k is between 2 and 5, practically. A higher power law represents a more severe loss. (Caution: power-law is not exponential) Besides distance, power loss also depends on frequency of the signal and the specific transmission medium. For example, higher-frequency radio waves generally suffer from higher power losses than their lower-frequency counterpart; thinner copper wires generally produce larger power attenuations than thicker copper wires; optical fibers offer much lower attenuations than copper wires/cables. 17
White noise is the most commonly used model for representing noise in communication systems. It is a random waveform whose power spectrum spreads across the entire useful frequency range in any medium where communication signals may exist. That is, there is no frequency region where noise level is less than the others. Typically, a filter is used at a communication receiver to remove the frequency components of noise that are outside the signal band, i.e., outside the frequency range of signal spectrum. The strength of noise is commonly represented by noise power (spectral) density N 0 expressed in Watt/Hz. The overall noise power that the received signal of interest is subject to, after the filtering, is thus P N = N 0 B where P N is in Watt, N 0 is in Watt/Hz, and B is in Hz. Let P s denote the received signal power (accounting for attenuation). The signal-tonoise ratio SNR = P s /P N is commonly used to represent reception quality of a communication system. Note: Power amplifier can boost P s but it can t boost the SNR. 18
Twisted pair phone wires was originally designed to support voice signals only. Its channel bandwidth (i.e., its passband) was treated as 4 khz (0-4 khz) then, enough to cover voice signals of all humans. Above 4 khz, the frequency response of twisted pair phone wires is lower and uneven. However, advanced electronics and digital signal processing technologies have made it possible to transport data signals over a less-than-desirable frequency range of the twisted-pair phone wires up to about 1.1 MHz. The usage of the higher-frequency band of these wires to send and receive data signals (known as DSL) does not conflict the legacy landline phone service (POTS) thus enabling the Telco to provide bundled voice and data services. 19
FYI: US cable TV spectrum allocation, Wireless EM frequency ranges, Optical fiber attenuation coefficient (db/km) versus wavelength. Wireless: higher frequency range more bandwidth available worst propagation characteristics (higher penetration loss, higher loss through rain/fog/cloud, etc.) Smaller wavelength thus smaller-sized antenna Optical fiber: three wavelength ranges (can be converted to frequency ranges by using c = f ) with low attenuation coefficients higher frequency response Fiber and laser samples. 20
The frequency response of a channel is practically imperfect: it is not flat enough (implying uneven frequency response) in the passband and it contains a transition band. As such, the signal is distorted because its sine wave components undergo different amplitude multipliers because of uneven frequency response within the signal bandwidth. This type of signal distortion caused by uneven frequency response of the channel is called linear distortion. The imperfect frequency response can be overcome by a technique called equalization : the idea is to feed the distorted signal into an equalizer a filter with a frequency response designed to equalize the channel frequency response. Mathematically, as shown in the graphical example, the product of the two frequency responses (multiplication of two functions of frequency) is an ideal frequency response: a constant within the frequency band of interest. 21
Another type of distortion called nonlinear distortion is not due to uneven treatment of different frequencies of the signal. In other words, it is not caused by imperfection of the frequency response of the channel. Recall that power attenuation is unavoidable when signal travels through a communication medium. As a signal waveform fluctuates, it strength rises and falls. If the channel attenuates stronger segments more than it does weaker segments, the received signal is distorted. This is called non-linear distortion. The phenomenon is analogous to the power gain unevenness of audio amplifiers: turning the volume too high results in distorted sound. For example, an 20-dB amplifier (x100) is supposed to boost audio signal by a power gain of G=100. But the output power of any audio amplifier is practically limited to a specified MAX output. Assume that the Max output of this 20-dB amplifier is 100 Watt. Then if the volume is tuned to an input level of say, 2 Watt, then the amplifier can produce a gain of at most 50. Thus, louder sound segments are amplified less than softer sound segments contrast is compromised. Typically, a channel has a linear operating range of input powers within which nonlinear distortion does not exist. Thus, the solution is to restrict the input power level such that it stays within the linear operating range of the channel. This represents one of the many power limitation factors in communication system and data network designs. 22
When applied to telephone communication systems, since different people speak with different loudness, the power compression algorithm used to restrict the input power level to the twisted pair telephone line has to account for that. In theory, we can identify the loudest person in the world and determine the scaling factor needed to lower his/her voice volume to the upper limit of the linear operating range of the telephone line and then apply that factor to all phone calls. Doing so will guarantee that everyone s voice is sufficiently suppressed to avoid nonlinear distortion. However, such an approach will render the soft talkers voice inaudible in the background of noise. Solution = companding: louder voices receive a high compression factor while lower voices receive a lower compression factor. To maintain contrast (since a person s voice volume rises and falls, the contrast conveys emotion), the compression process is reversed at reception with an expanding process using an inverse nonlinear function of the compression function. Note: the slope of the nonlinear curve at a given power level indicates the power gain offered by the device at that power level 23