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The imperfection causes signal impairment. Below are the causes of the impairment.
Processing and transmission of timing signals in synchronous networks. Luciano Gualberto, travessa 3, n. In order to have accurate operation, synchronous telecommunication networks need a reliable time basis signal extracted from the line data stream in each node. When the nodes are synchronized, routing and detection can be performed, guaranteeing the correct sequence of information distribution among the several users of a transmission trunk. Consequently, an auxiliary network is created inside the main network, a sub-network, dedicated to the distribution of the clock signals.
Chapter 3: Analysis and Transmission of Signals 3. Fourier Transform The motivation for the Fourier transform comes from the study of Fourier series. In Fourier series complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. Due to the properties of sine and cosine it is possible to recover the amount of each wave in the th sum b an i t by integral.
Fourier Transform From sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex valued. Complex number gives both the amplitude or size of the wave present in the function and the phase or the initial angle of the wave.
The Fourier series can only b used f Th F i i l be d for periodic i di signals. Fourier Transform How can the results be extended for Aperiodic signals such as g t of limited length T?
To is made long enough to avoid overlapping between the repeating pulses. Observe that the nature of the spectrum changes as To increases. Let us define G w ; a g continuous function of Then 8. Doubling To halves the fundamental frequency o, so that there are now twice as many samples in the spectrum.
Fourier Transform The sum on the right-hand side can be viewed as the area under the function G w ejt. Fourier Transform G w is complex. To plot the spectrum G w as a function of , we have both amplitude and phase spectra:. For real g t , The amplitude spectrum is an even function The phase spectrum g 17is an odd function of. Unit Triangle Function A unit triangle function x has a unit height and a unit width centered at the origin.
The trigonometric spectrum positive frequencies. The negative frequencies occur because we use exponential spectra for mathematical convenience. Each sinusoid coswnt appears of two exponential compnents with frequencies wn and w-n.
In reality there is only frequency which is the wn. It is also known as the filtering or interpolating function. Example 3. The scaling property states that the time compression of a signal results in its spectral expansion, and time expansion of the signal results in its spectral compression.
In practice frequency shift multiplying g t by a sinusoid as: is achieved by. Scaling Property Multiplication of a sinusoid cos wot by g t amounts to modulating the sinusoid amplitude.
This type of modulation is called amplitude modulation. The signal g t is called the modulating signal. To sketch g t cos wot. The transmission of an input signal g t through a system changes it into the output signal y t. G w and Y w are the spectra of the input and the output. H w is the spectral response of the system. Distortionless Transmission Transmission is said to be distortionless if the input and the output have identical wave shapes within a mu p multiplicative constant.
A delayed output that retains the input waveform is also considered distortionless. Thus, in distortionless transmission, the input g t and the output y t satisfy the condition. Ideal and Practical Filters The ideal high-pass and characteristics are shown below. The impulse response h t is not realizable. If td is sufficiently large, h t will be a close approximation of h t , and the resulting filter ii w pp , g will be a good approximation of an ideal filter.
Ideal and Practical Filters The truncation operation [cutting the tail of h t to make it causal], however, creates some unsuspected problems of spectral spread and leakage This can be partly corrected by truncating h t gradually rather than abruptly using a tapered window function.
Practical realizable filter characteristics gradual, without jump discontinuities in amplitude response H w. Butterworth Filters The well-known Butterworth filters, for example, have amplitude response. The amplitude response approaches an ideal low-pass behavior as n. Also called cutoff frequency. As n, the amplitude response approaches ideal, but the corresponding phase response is badly distorted in the vicinity of the cutoff frequency B Hz.
A certain trade-off exists 92 between ideal magnitude and ideal phase characteristics. Linear Distortion Signal distortion can be caused over a linear timeinvariant channel by nonideal characteristics of either the magnitude, the phase, or both. If a pulse g t l t is transmitted i t itt d through such a th h h channel. Spreading, or dispersion, of the pulse will occur if either the amplitude response or the phase response, or both, are nonideal.
Linear Distortion A distortionless channel multiplies each component by h b the same f factor and d l d delays each component b h by the same amount of time. If the amplitude response of the channel is not ideal [that is, H w is not equal to a constant], then the pulse will spread out see the following example. Linear Distortion Dispersion of the pulse is undesirable in a TDM system, because pulse spreading causes interference with a neighboring pulse and consequently with a neighboring channel crosstalk.
For an FDM system, this type of distortion causes distortion dispersion in each multiplexed signal, but no interference occurs with a neighboring channel channel. This is because in FDM, each of the multiplexed signals occupies a band not occupied by any other signal. It consists of g t and its echoes shifted by td.
The dispersion of the pulse caused by its echoes is evident from the figure below. Distortion Caused by Channel Nonlinearities We shall consider a simple case of a memoriless nonlinear channel where the input g and the output y are related by some nonlinear equation,. If the bandwidth of g t is B Hz, then the bandwidth of gk t is kB Hz. Then, the bandwidth of y t is kB Hz Hz.
The output spectrum spreads well beyond the input spectrum, and the output signal contains new frequency components not contained in the input signal. If a signal is transmitted over a nonlinear channel channel, the nonlinearity not only distorts the signal, but also causes interference with other signals on the channel because of its spectral dispersion spreading which will cause a serious interference problem in FDM systems but not in TDM systems.
Verify that the bandwidth of the output signal is twice that of the input signal This is the result signal. Can the signal x t be recovered distortion from the output y t? Note that the desired signal and the distortion signal spectra overlap, and it is impossible to recover the signal x t from the received signal y t without some distortion.
Observe that the output of this filter is the desired input signal x t with some residual distortion. We have an additional problem of interference with other signals if the input signal x t is frequency-division multiplexed along with several other signals on this channel. This means that several signals occupying nonoverlapping frequency bands are transmitted simultaneously on the same channel. Thus, in addition to the distortion of x t , we also have an interference with the neighboring band.
If x t were a digital signal consisting of a pulse train, each pulse would be distorted, but there would be no interference with the neighboring pulses. Moreover even with distorted pulses, data can be received without loss because digital communication can withstand considerable pulse distortion without loss of information. Thus, Thus if this channel were used to transmit a TDM signal consisting of two interleaved pulse trains, the data in the two trains would be recovered at the receiver.
Distortion Caused by Multipath Effects A multipath transmission takes place when a transmitted signal arrives at the receiver by two or more paths of different delays. In radio links, the signal can be received by direct path between the transmitting and the receiving antennas and also by reflections from other objects, such as hills, buildings, and so on. In this case the transmission channel can be represented as several channels in parallel, each with a different relative attenuation and a different time delay.
The overall transfer function of such a channel is H w , given by. Distortion Caused by Multipath Effects The multipath transmission, therefore, causes nonidealities in the magnitude and the phase characteristics of the channel and will cause linear distortion pulse dispersion.
If the gains of the two paths are very close, that is, 1, the signals received by the two paths can very nearly cancel each other at certain frequencies, y y q where their phases are rad apart destructive interference. These frequencies are the multipath null frequencies. Such channels cause frequency-selective fading of transmitted signals Such distortion can be partly signals. Fading Channels Thus far, the channel characteristics were assumed , to be constant with time.
In practice, we encounter channels whose transmission characteristics vary with time. These include troposcatter channels and channels using the ionosphere for radio reflection to achieve longdistance communication. The time variations of the channel properties arise because of semiperiodic and random changes in the propagation characteristics of the medium.
Fading Channels The reflection properties of the ionosphere, for example, example are related to meteorological conditions that change seasonally, daily, and even from hour to hour, much the same way as does the weather. Periods of sudden storms also occur. Hence, the effective channel transfer function varies semiperiodically and randomly, causing random attenuation of the signal This phenomenon is known signal.
One way to reduce the effects of fading is to use automatic gain control AGC. Fading Channels Fading may be strongly frequency dependent where different frequency components are affected unequally. Such fading is known as frequencyselective fading and can cause serious problems in communication.
Multipath propagation can cause frequency-selective fading. Signal Energy and Energy Spectral Density The energy Eg of a signal g t is defined as the area under lg t l2 We can also determine the signal energy from its Fourier transform G w through Parseval's theorem. Signal energy can be related to the signal spectrum G w by:. Essential Bandwidth of a Signal Most of the signal energy is contained within a certain band of B Hz.
Therefore, we can supress the signal spectrum beyond B Hz with little effect on the signal shape and energy. The bandwidth B is called the essentail bandwidth of the signal. This means that all the remaining spectral components in the band from Note that Energy of Modulated Signals Let g t be a baseband signal band-limited to b-Hz. The amplitude modulation t is:. Time Autocorrelation Function and the Energy Spectral Density For a real signal g t , the autocorrelation function g is given by:.
Chapter 3: Analysis and Transmission of Signals 3. Fourier Transform The motivation for the Fourier transform comes from the study of Fourier series. In Fourier series complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. Due to the properties of sine and cosine it is possible to recover the amount of each wave in the th sum b an i t by integral. Fourier Transform From sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex valued. Complex number gives both the amplitude or size of the wave present in the function and the phase or the initial angle of the wave. The Fourier series can only b used f Th F i i l be d for periodic i di signals.
JavaScript seems to be disabled in your browser. For the best experience on our site, be sure to turn on Javascript in your browser. A Plus account is required to perform this action. Get valuable resources straight to your inbox - sent out once per month. A signal is an electromagnetic or electrical current that carries data from one system or network to another. In electronics, a signal is often a time-varying voltage that is also an electromagnetic wave carrying information, though it can take on other forms, such as current.
Chapter 3: Analysis and Transmission of Signals 3. Fourier Transform The motivation for the Fourier transform comes from the study of Fourier series. In Fourier series complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. Due to the properties of sine and cosine it is possible to recover the amount of each wave in the th sum b an i t by integral. Fourier Transform From sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex valued.
A communications system or communication system is a collection of individual telecommunications networks , transmission systems, relay stations, tributary stations, and terminal equipment usually capable of interconnection and interoperation to form an integrated whole. The components of a communications system serve a common purpose, are technically compatible, use common procedures, respond to controls, and operate in union. Telecommunications is a method of communication e. Communication is the act of conveying intended meanings from one entity or group to another through the use of mutually understood signs and semiotic rules.
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The communication that occurs in our day-to-day life is in the form of signals. These signals, such as sound signals, generally, are analog in nature. When the communication needs to be established over a distance, then the analog signals are sent through wire, using different techniques for effective transmission. The conventional methods of communication used analog signals for long distance communications, which suffer from many losses such as distortion, interference, and other losses including security breach. In order to overcome these problems, the signals are digitized using different techniques. The digitized signals allow the communication to be more clear and accurate without losses. The following figure indicates the difference between analog and digital signals.
Chapter 3: Analysis and Transmission of Signals3. Fourier Transform The motivation for the Fourier transform comes from the study of Fourier series. In Fourier series complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. Due to the properties of sine and cosine it is possible to recover the amount of each wave in the th sum b an i t by integral. Fourier Transform From sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex valued. Complex number gives both the amplitude or size of the wave present in the function and the phase or the initial angle of the wave. The Fourier series can only b used f Th F i i l be d for periodic i di signals.
EMG signals acquired from muscles require advanced methods for detection, decomposition, processing, and classification.
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