Example 82
There are many ways to translate data into binary equivalents. Example 8.1 showed one way to convert text into 4-PAM and then into binary. Another way exploits the Matlab function text2bin. m and its inverse bin2text. m, which use the 7-bit version of the ASCII code rather than the 8-bit version . This representation is more efficient, since each pair of text letters can be represented by 14 bits or seven 4-PAM symbols rather than 16 bits or eight 4-PAM symbols . On the other hand, the 7 bit...
or for JLsa
0 1000 000 3000 4000 5000 8000 7000 8000 3000 1 0000 0 1000 000 3000 4000 5000 8000 7000 8000 3000 1 0000 0 1000 ZKJO 3000 4000 5000 6000 7000 8000 9000 10000 0 1000 ZKJO 3000 4000 5000 6000 7000 8000 9000 10000 0 1000 2000 3000 4000 5000 6000 70110 8000 9000 10W0 FIGURE 6.13 An automatic gain control adjusts the parameter a in the top panel automatically to achieve the desired output power. Perhaps the best way to formally describe how the algorithms work is to plot the performance functions....
Problems 1
6.15. Explore the behavior of steepest descent by running polyconverge .m with different a Try mu -.01, 0, .0001, .02, .03, .05, 1.0, 10.0. Can mu be too large or too small b Try N 5, 40, 100, 5000. Can N be too large or too small c Try a variety of values of x l . Can x l be too large or too small As an alternative to simulation, observe that the process 6.6 is itself a linear time invariant system, of the general form which is stable as long as a lt 1. For a constant input, the final value...
vk
FIGURE 5.5 AM suppressed carrier communication system a the transmitter modulator, b the receiver demodulator. Suppose that the frequency of the modulator is fc but that the frequency at the receiver is fc 7, for some small 7. Similarly, suppose that the phase of the modulator is 0 but that the phase at the receiver is lt f gt . Figure 5.5 b shows this downconverter, which can be described as x t v t cos 27r c j t lt f gt 5.2 where LPF represents a low pass filtering of the demodulated signal x...
sm
FIGURE 4.10 The magnitude spectrum of a message signal w t is shown in a . When w t is modulated by a cosine at frequency c, the spectrum of the resulting signal s t w t cos 27rfct lt j gt is shown in b . response scaled by the size of the input and shifted to begin at time A. The complete output is then given by summing over all A. Since there is a continuum of possible values of A, this sum is actually an integral, and the output is x X h t - X dX x t h t . 4.8 This integral defines the...
r c
narrow city street, or in a mobile device such as a cell phone the operator might turn a corner and cause a large change in the local geometry of reflections. Fading may also occur when the transmitter and or the receiver are moving. The Doppler effect shifts the frequencies slightly, causing interferences that may slowly change. Such time varying problems cannot be fixed by a single fixed filter, rather, the filter must somehow compensate differently at different times. This is an ideal...
Simulating The Ideal System
The simulation of the digital communication system in Figure 9.1 divides into two parts just as the figure does. The first part creates the analog transmitted signal, and the second part implements the discrete-time receiver. The message consists of the character string 01234 I wish I were an Oscar Meyer wiener 56789 In order to transmit this important message, it is first translated into the 4-PAM symbol set 1, 3 which is designated m i for i 1,2, , N using the subroutine letters2pam. This can...
magnitude spectrum shows the frequency content of the output signal
FIGURE 3.1 The element transforms the input signal x into the output signal y. The action of an element can be thought of in terms of its effect on the signals in time, or via the Fourier transform in terms of its effect on the spectra of the signals. Readers who have studied signal and systems often required in electrical engineering degrees , will recognize that the time domain representation of a signal and its frequency domain representation are related by the Fourier transform, which is...
Correlation
Suppose there are two signals or sequences. Are they similar, or are they different If one is just shifted in time relative to the other, how can the time shift be determined The approach called correlation shifts one of the sequences in time, and calculates how well they match by multiplying point by point and summing at each shift. When the sum is small then they are not much alike when the sum is large, many terms are similar. Thus correlation is a simple form of pattern matching, which is...
Timing Recovery
All we have to decide is what to do with the time given us. - Gandalf, in J. R. R. Tolkien's Fellowship of the Ring When the signal arrives at the receiver, it is a complicated analog waveform that must be sampled in order to eventually recover the transmitted message. The timing offset experiments of Section 9.4.5 showed that one kind of stuff that can happen to the received signal is that the samples might inadvertently be taken at inopportune times. The eye becomes closed and the symbols are...
Problems Kgx
7.4. Which column C8- represents the highest possible frequency in the DFT What do the elements of this column look like Hint Look at Cjy and think of a square wave. This square wave is the highest frequency that can be represented by the DFT, and occurs at exactly the Nyquist rate. 4Since W N n by the discrete version of the symmetry property A.35 , the magnitudes are equal but the phases have opposite signs. Fortunately, Matlab makes it easy to do spectral analysis with the DFT by providing a...
Digital Filtering And The Dft
Digital filtering is not simply converting from analog to digital filters it is a fundamentally different way of thinking about the topic of signal processing, and many of the ideas and limitations of the analog method have no counterpart in digital form. - R. W. Hamming, Digital Filters, 3rd edition, Prentice Hall 1989. Once the received signal is sampled, the real story of the digital receiver begins. An analog bandpass filter at the front end of the receiver removes extraneous signals for...
F2 Sketching The Frequency Response From The Ztransform
A complex number a a jb can be drawn in the complex plane as a vector from the origin to the point a,b . Figure F.l gives a graphical illustration of the difference between two complex numbers 3 a, which is equal to the vector drawn from a to 3. The magnitude is the length of this vector, and the angle is measured counterclockwise from the horizontal drawn to the right of a to the direction of 3 a, as shown. FIGURE F.l Graphical calculation of the difference between two complex numbers As with...
A Design Methodology For The M6 Receiver
Before describing the specific design requirements that must be met by a successful M6 receiver, this section makes some generic remarks about a systematic approach to receiver design. There are four generic stages 1. Choose the order in which the basic operations of the receiver occur. 2. Select components and methods that can perform the baste operations in an ideal setting. 3. Select adaptive elements that allow the receiver to continue functioning when there are impairments. 4. Verify that...
Linear Equalization
The revolution in data communications technology can be dated from the invention of automatic and adaptive channel equalization in the late 1960s. Gitlin, Hayes, and Weinstein, Data Communication Principles, 1992. When all is well in the receiver, there is no interaction between successive symbols each symbol arrives and is decoded independently of all others. But when symbols interact, when the waveform of one symbol corrupts the value of a nearby symbol, then the received signal becomes...
A Telecommunication System
The reason digital radio is so reliable is because it employs a smart receiver. Inside each digital radio receiver there is a tiny Computer a computer capable of sorting through the myriad of reflected and atmospherically distorted transmissions and reconstructing a solid, usable signal for the set to process. from 2 2 03 Telecommunications technologies using electromagnetic transmission surround us television images flicker, radios chatter, cell phones and telephones ring, allowing us to see...
Kx
FIGURE 10.10 The Costas loop is a phase tracking algorithm based on the performance function 10.13 . Suppose that a 4-PAM transmitted signal r is created as in pulrecsig.m from page 196 with carrier frequency f0 1000. Then the Costas loop phase tracking method 10.15 can be implemented in much the same way that the PLL was implemented in pllconverge .m. costasloop.m costas loop - input rsc from pulrecsig.m initialize estimate vector initialize buffers for LPFs z's contain past fl 1 inputs f 1...
Problems Cow
15.12. Find the amplitudes of the iV-level equally spaced signal with unity power when 15.13. Use noisychan.m to compare the noise performance of 2-level, 4-level, and 6-level transmissions. a Modify the program to generate 2 and 6-level signals. b Make a plot of the noise power versus the percentage of errors for 2, 4, and 6-level. 15.14. Use noisychan.m to compare the power requirements for 2-level, 4-level, and 6-level transmissions. Fix the noise power at p 0.01, and find the error...
Problems Shc
7.19. In Exercise 7.10, the program specgong.m was used to analyze the sound of an Indonesian gong. The three most prominent partials or narrowband components were found to be at about 520, 630, and 660 Hz. a Design a filter using remez that will remove the two highest partials from this sound without effecting the lowest partial. b Use the filter command to process the gong.wav file with your filter. c Take the FFT of the resulting signal the output of your filter and verify that the partial...
Power Spectral Density
One way of classifying and measuring signals and systems is by their power or energy , and the amount of power or energy in various frequency regions. This section defines the power spectral density, and shows how it can be used to measure the power in signals, to measure the correlation within a signal, and to talk about the gain of a linear system. In Telecommunication Breakdown, power spectral density is used mainly in Chapter 11 in the discussion of the design of matched filtering. The time...
decision device
FIGURE 14.5 Trained Adaptive Linear Equalizer When all goes well, the recursive algorithm 14.27 converges to the vicinity of the block least-squares answer for the particular used in forming the delayed recovery error. As long as 1 is nonzero, if the underlying composition of the received signal changes so that the error increases and the desired equalizer changes, then the f react accordingly. It is this tracking ability that earns it the label adaptive4. The following Matlab code implements...
Pulse Shaping And Receive Filtering
See first that the design is wise and just that ascertained, pursue it resolutely do not for one repulse forego the purpose that you resolved to effect. - William Shakespeare When the message is digital, it must be converted into an analog signal in order to be transmitted. This conversion is done by the transmit or pulse-shaping filter, which changes each symbol in the digital message into a suitable analog pulse. After transmission, the receive filter assists in recapturing the digital values...
The Fourier Transform And Its Inverse
By definition, the Fourier transform of a time function w t is which appeared earlier in Equation 2.1 . The Inverse Fourier transform is Observe that the transform is an integral over all time, while the inverse transform is an integral over all frequency the transform converts a signal from time into frequency, while the inverse converts from frequency into time. Because the transform is invertible, it does not create or destroy information. Everything about the time signal w t is contained in...
symbols
Eye diagram for the 2T-wide hamming pulse shape FIGURE 11.7 Eye diagrams for T, 2T, 3T, and 5T-wide Hamming pulse shapes show how the sensitivity to noises and timing errors increases as the pulse shape widens. The closed-eye in the bottom plot means that symbol errors are inevitable. shape in the top plot uses ps ones l,M , the Hamming pulse shape in the middle uses ps hamming M , and the bottom plot uses a truncated sine pulse shape ps SRRC L,0,M for L 10. The rectangular pulse is insensitive...
Example G4
Example G.2 assumes that the parameter ai of the linear filter is fixed, even though the purpose of the adaptation is to allow ai to change in response to the behavior of the signal. Let cr j3 k , k be formed by filtering a signal u k that is independent of 3 k , To be precise, let 3 k ai k and cr j3 k ,k cr ai k , k ao amp amp ai k u k 1 ci2 k u k 2 . Suppose also that the dynamics of ai k are given by ai k ai k 1 nj ai k 1 , k 1 . Then the approximation G.17 yields bi ao k i u k i ai k i u k...