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systems analysis and design using matlab

Questions and Answers of Systems Analysis And Design Using MATLAB

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
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
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)
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------  –
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
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 .
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
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
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
.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
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
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)
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
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.
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 .

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