New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
business
systems analysis and design using matlab
Radar Systems Analysis And Design Using MATLAB 1st Edition Bassem R. Mahafza - Solutions
7.9. Compute the discrete autocorrelation for an Frank code.
7.10. Generate a Frank code of length 8, .q = 11 γ = 2 N = 10 x(n)s(t) = r(t) cos (2πf0t)r(t) = x(0), for 0 < t < Δt r(t) = x(n), for nΔt < t < (n + 1)Δt r(t) = 0, for t > 7Δt Δt = 0.5μs s(t)s(t – 10Δt)φ11 N = 13 k = 6 B75 B57 F16 F8
8.1. Using Eq. (8.4), determine when and .
8.2. An exponential expression for the index of refraction is given by where the altitude is in Km. Calculate the index of refraction for a well mixed atmosphere at 10% and 50% of the troposphere.
8.3. Rederive Eq. (8.34) assuming vertical polarization.
8.4. Reproduce Figs. 8.6 and 8.7 by using and (a)and (dry soil); (b) and (sea water at ); (c)and (lake water at ).
8.5. In reference to Fig. 8.9, assume a radar height of and a target height of . The range is . (a) Calculate the lengths of the direct and indirect paths. (b) Calculate how long it will take a pulse to reach the target via the direct and indirect paths.
8.6. In the previous problem, assuming that you may be able to use the small grazing angle approximation: (a) Calculate the ratio of the direct to the indirect signal strengths at the target. (b) If the target is closing on the radar with velocity , calculate the Doppler shift along the direct and
8.7. Utilizing the plots generated in solving Problem 8.4, derive an emperical expression for the Brewster’s angle.
8.8. A radar at altitude and a target at altitude , and assuming a spherical earth, calculate , , and .
8.9. Derive an asymptotic form for and when the grazing angle is very small.
8.10. In reference to Fig. 8.8, assume a radar height of and a target height of . The range is . (a) Calculate the lengths of the direct and indirect paths. (b) Calculate how long it will take a pulse to reach the target via the direct and indirect paths.
8.11. Using the law of cosines, derive Eqs. (8.51) through (8.53).
8.12. In the previous problem, assuming that you may be able to use the small grazing angle approximation: (a) Calculate the ratio of the direct to the indirect signal strengths at the target. (b) If the target is closing on the radar with velocity , calculate the Doppler shift along the direct and
8.13. In the previous problem, assuming that you may be able to use the small grazing angle approximation: (a) Calculate the ratio of the direct to the indirect signal strengths at the target. (b) If the target is closing on the radar with velocity , calculate the Doppler shift along the direct and
8.14. Calculate the range to the horizon corresponding to a radar at and of altitude. Assume 4/3 earth.
8.15. Develop a mathematical expression that can be used to reproduce Figs. 8.14 and 8.15.
9.1. Compute the signal-to-clutter ratio (SCR) for the radar described in Example 9.1. In this case, assume antenna 3dB beam width , pulse width , range , grazing angle , target RCS , and clutter reflection coefficient .
9.2. Repeat Example 9.2 for target RCS , pulse width, antenna beam width ; the detection range is , and .θ3dB = 0.03radτ = 10μs R = 50Km ψg = 15°σt 0.1m2 = σ0 0.02 m2 m2 = ( ⁄ )σt 0.15m2 =τ = 0.1μs θa θe = = 0.03radians R = 100Km σΣ i 1.6 10 –9 × m2 m3 = ( ⁄ )
9.3. The quadrature components of the clutter power spectrum are, respectively, given by Compute the D.C. and A.C. power of the clutter. Let .
9.4. A certain radar has the following specifications: pulse width, antenna beam width , and wavelength . The radar antenna is high. A certain target is simulated by two point targets(scatterers). The first scatterer is high and has RCS . The second scatterer is high and has RCS . If the target is
9.5. A certain radar has range resolution of and is observing a target somewhere in a line of high towers each having RCS . If the target has RCS , (a) How much signal-to-clutter ratio should the radar have? (b) Repeat part a for range resolution of .
9.7. One implementation of a single delay line canceler with feedback is shown below:(a) What is the transfer function, ? (b) If the clutter power spectrum is, find an exact expression for the filter power gain.(c) Repeat part b for small values of frequency, . (d) Compute the clutter attenuation
9.8. Plot the frequency response for the filter described in the previous problem for .
9.9. An implementation of a double delay line canceler with feedback is shown below:(a) What is the transfer function, ? (b) Plot the frequency response for, and .
9.10. Consider a single delay line canceler. Calculate the clutter attenuation and the improvement factor. Assume that and a PRF.
9.11. Develop an expression for the improvement factor of a double delay line canceler.
9.12. Repeat Problem 9.10 for a double delay line canceler.
9.13. An experimental expression for the clutter power spectrum density is, where is a constant. Show that using this expression leads to the same result obtained for the improvement factor as developed in Section 9.11.
9.14. Repeat Problem 9.13 for a double delay line canceler.
9.15. A certain radar uses two PRFs with stagger ratio 63/64. If the first PRF is , compute the blind speeds for both PRFs and for the resultant composite PRF. Assume .
9.16. A certain filter used for clutter rejection has an impulse response. (a) Show an implementation of this filter using delay lines and adders. (b) What is the transfer function?(c) Plot the frequency response of this filter. (d) Calculate the output when the input is the unit step sequence.
9.17. The quadrature components of the clutter power spectrum are given in Problem 9.3. Let and . Compute the improvement of the signal-to-clutter ratio when a double delay line canceler is utilized.K = –0.5, 0, and 0.5-+x(t) Σ y (t)Σ d elay, T+ +K 2+- + Σ d elay, T K 1 H(z)K1 = 0 = K2 K1 =
9.18. Develop an expression for the clutter improvement factor for single and double line cancelers using the clutter autocorrelation function. Assume that the clutter power spectrum is as defined in Eq. (9.65).
10.1. Consider an antenna whose diameter is . What is the far field requirement for an X-band or an L-band radar that is using this antenna?
10.2. Consider an antenna with electric field intensity in the xy-plane. This electric field is generated by a current distribution in the yzplane.The electric field intensity is computed using the integral where is the wavelength and is the aperture. (a) Write an expression for when (a constant).
10.3. A linear phased array consists of 50 elements with element spacing. (a) Compute the 3dB beam width when the main beam steering angle is and . (b) Compute the electronic phase difference for any two consecutive elements for steering angle .
10.4. A linear phased array antenna consists of eight elements spaced with element spacing. (a) Give an expression for the antenna gain pattern(assume no steering and uniform aperture weighting). (b) Sketch the gain pattern versus sine of the off boresight angle . What problems do you see is using
10.5. In Section 10.6 we showed how a DFT can be used to compute the radiation pattern of a linear phased array. Consider a linear of 64 elements at half wavelength spacing, where an FFT of size 512 is used to compute the pattern.What are the FFT bins that correspond to steering angles ?d = 3m
11.1. Show that in order to be able to quickly achieve changing the beam position the error signal needs to be a linear function of the deviation angle.
11.2. Prepare a short report on the vulnerability of conical scan to amplitude modulation jamming. In particular consider the self-protecting technique called “Gain Inversion.”
11.3. Consider a conical scan radar. The pulse repetition interval is .Calculate the scan rate so that at least ten pulses are emitted within one scan.
11.4. Consider a conical scan antenna whose rotation around the tracking axis is completed in 4 seconds. If during this time 20 pulses are emitted and received, calculate the radar PRF and the unambiguous range.
11.5. Reproduce Fig. 11.11 for radians.
11.6. Reproduce Fig. 11.13 for the squint angles defined in the previous problem.
11.7. Derive Eq. (11.33) and Eq. (11.34).
11.8. Consider a monopulse radar where the input signal is comprised of both target return and additive white Gaussian noise. Develop an expression for the complex ratio .
11.9. Consider the sum and difference signals defined in Eqs. (11.7) and(11.8). What is the squint angle that maximizes ?
11.10. A certain system is defined by the following difference equation:Find the solution to this system for and .
11.11. Prove the state transition matrix properties (i.e., Eqs. (11.30) through(11.36)).
11.12. Suppose that the state equations for a certain discrete time LTI system are If , find when the input is a step function.
11.13. Derive Eq. (11.55).
11.14. Derive Eq. (11.75).
11.15. Using Eq. (11.83), compute a general expression (in terms of the transfer function) for the steady state errors when the input sequence is:
11.16. Verify the results in Eqs. (11.99) and (11.100).
11.17. Develop an expression for the steady state error transfer function for an tracker.
11.18. Using the result of the previous problem and Eq. (11.83), compute the steady-state errors for the tracker with the inputs defined in Problem
11.13.
11.19. Design a critically damped , when the measurement noise variance associated with position is and when the desired standard deviation of the filter prediction error is .
11.20. Derive Eqs. (11.118) through (11.120).
11.21. Derive Eq. (11.122).
11.22. Consider a filter. We can define six transfer functions: ,, , , , and (predicted position, predicted velocity, predicted acceleration, smoothed position, smoothed velocity, and smoothed acceleration). Each transfer function has the form The denominator remains the same for all six transfer
11.23. Verify the results obtained for the two limiting cases of the Singer-Kalman filter.
11.24. Verify Eq. (11.160).
12.1. A side looking SAR is traveling at an altitude of ; the elevation angle is . If the aperture length is , the pulse width is and the wavelength is . (a) Calculate the azimuth resolution.(b) Calculate the range and ground range resolutions.
12.2. A MMW side looking SAR has the following specifications: radar velocity , elevation angle , operating frequency, and antenna 3dB beam width . (a) Calculate E(u)W'(p, q)2πNa------ – p 2πλ= ------dsinβcosα2πNa------ – q 2πλ= ------dsinβsinαα q p--
12.3. A side looking SAR takes on eight positions within an observation interval. In each position the radar transmits and receives one pulse. Let the distance between any two consecutive antenna positions be , and define to be the one-way phase difference for a beam steered at angle . (a) In each
12.4. Consider a synthetic aperture radar. You are given the following Doppler history for a scatterer: which corresponds to times . Assume that the observation interval is, and a platform velocity . (a) Show the Doppler history for another scatterer which is identical to the first one except that
12.5. You want to design a side looking synthetic aperture Ultrasonic radar operating at and peak power . The antenna beam is conical with 3dB beam width . The maximum gain is . The radar is at a constant altitude and is moving at a velocity of . The elevation angle defining the footprint is . (a)
12.6. Derive Eq. (12.45) through Eq. (12.47).
12.7. In Section 12.7 we assumed the elevation angle increment is equal to zero. Develop an equivalent to Eq. (12.43) for the case when . You need to use a third order three-dimensional Taylor series expansion about the state in order to compute the new round-trip delay expression.
13.1. Classify each of the following signals as an energy signal, as a power signal, or as neither. (a) ; (b) ; (c); (d) .
13.2. Compute the energy associated with the signal .
13.3. (a) Prove that and , shown in Fig. P13.3, are orthogonal over the interval . (b) Express the signal as a weighted sum of and over the same time interval.
13.4. A periodic signal is formed by repeating the pulse every 10 seconds. (a) What is the Fourier transform of. (b) Compute the complex Fourier series of ? (c) Give an expression for the autocorrelation function and the power spectrum density
.13.5. If the Fourier series is define . Compute an expression for the complex Fourier series expansion of .
13.6. Show that (a) . (b) If and, then , where the average values for and are zeroes.
13.7. What is the power spectral density for the signal
13.8. A certain radar system uses linear frequency modulated waveforms of the form What are the quadrature components? Give an expression for both the modulation and instantaneous frequencies.
13.9. Consider the signal and let and . What are the quadrature components?
13.10. Determine the quadrature components for the signal
13.11. If , determine the autocorrelation functions and when .
13.12. Write an expression for the autocorrelation function , where and . Give an expression for the density function.
13.13. Derive Eq. (13.52).
13.14. An LTI system has impulse response(a) Find the autocorrelation function . (b) Assume the input of this system is . What is the output?
13.15. Suppose you want to determine an unknown DC voltage in the presence of additive white Gaussian noise of zero mean and variance .The measured signal is . An estimate of is computed by making three independent measurements of and computing the arithmetic mean, . (a) Find the mean and variance
13.16. Consider the network shown in Fig. P13.16, where is a random voltage with zero mean and autocorrelation function .Find the power spectrum . What is the transfer function? Find the power spectrum .x(t) = x1(t) – 2x1(t – 5) + x1(t – 10)Rx1(t) Rx(t) x1(t) t2 = exp(– ⁄ 2)Ry(t)y(t)
13.17. (a) A random voltage has an exponential distribution function where . The expected value. Determine .
13.18. Assume the and miss distances of darts thrown at a bulls-eye dart board are Gaussian with zero mean and variance . (a) Determine the probability that a dart will fall between and . (b) Determine the radius of a circle about the bulls-eye that contains 80% of the darts thrown. (c)Consider a
13.19. Let be the PSD function for the stationary random process. Compute an expression for the PSD function of.
13.20. Let be a random variable with(a) Determine the characteristic function . (b) Using , validate that is a proper pdf. (c) Use to determine the first two moments of . (d) Calculate the variance of .
13.21. Let be a stationary random process, and the autocorrelation .
13.22. In Fig. 13.1, let Give an expression for .
13.23. Compute the Z-transform for(a) ; (b) .
13.24. (a) Write an expression for the Fourier transform of(b) Assume that you want to compute the modulus of the Fourier transform using a DFT of size 512 with a sampling interval of 1 second. Evaluate the modulus at frequency . Compare your answer to the theoretical value and compute the error.
13.25. A certain band-limited signal has bandwidth . Find the FFT size required so that the frequency resolution is . Assume radix 2 FFT and record length of 1 second.
13.26. Assume that a certain sequence is determined by its FFT. If the record length is and the sampling frequency is , find .
Showing 2600 - 2700
of 2697
First
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Step by Step Answers
Get 50% OFF
Claim Now
