- Redraw the inertial measurement system context diagram in Figure 4.14 to take into account calibration and diagnostic modes. 10 C: 16-Nov-2012 17:12:04 De Action EW.WE M-S 3 DONT DONT Do Action/d De
- From the definition of the DFTone can obtain a matrix equation X = Fx.(a) Suppose that N = 2 and x[n] = 1 for n = 0, 1, express the DFT as a matrix equation.(b) Check if the matrix Fin your
- The impulse response of a LTI discrete-time system is h[n] = u[n] − u[n − 3]. If the input to this system is(a) Find the output y[n]of this system by calculating graphically the convolution
- The convolution sum is a fast way to find the coefficients of the polynomial resulting from the multiplication of two polynomials.(a) Suppose x[n] = u[n] − u[n − 3] find its Z-transform
- Can the number of instructions executed serve as a timer mechanism in a real-time operating system? How?
- Derive the look-up table for the tangent function in increments of 1 degree. Be sure to take advantage of symmetry.
- What is the range of an unsigned scaled 16-bit number with least significant bit −0.00043?
- Write a program in the language of your choice, which takes an arbitrary function and table increment and writes a look-up table functional. The arbitrary function will have to be hard-coded into the
- A periodic task τi with phase φi , period pi , execution time ei , and relative deadline Di is represented by the 4-tuple (φi, pi, ei,Di ) . For example, (1, 10, 3, 6) is a periodic task whose
- What unique challenges are presented in performance analysis for the example systems described in Chapter 1? Namely:(a) Inertial measurement system(b) Nuclear monitoring system(c) Airline reservation
- Research the use of McCabe’s metric in real-time systems by searching theliterature.
- For the inertial measurement system, which testing approaches would you use? When and why?
- If the inertial measurement system were written in C++ according to the design fragment described in Chapter 5, describe the testing strategy you would use. If possible, try to design some test cases.
- Can the tools available impact the software project and the code quality? How?
- For the example systems already described:• Nuclear monitoring system• Inertial measurement system• Airline reservation system• Pasta sauce bottling system• Traffic light control system
- Consider the statement “good real-time engineering is not good for software engineering and vice versa.” Do you consider this statement true or false? Justify your answer with sufficient examples.
- Use statecharts instead of finite state machines to represent the visual inspection system as it is described in the examples. Do the same using Petri nets instead.
- Redraw the use-case diagram for the IMU in Figure 4.15 to include calibration and diagnostic modes. Figure 4.15 Temp Sensors IMU Compute and display true position Visual Display Unit Control and
- Discuss the advantages of built-in-test software in enhancing fault-tolerance capabilities of real-time systems.
- Using a data flow diagram, design a process controller for an environment monitoring system that collects data from a set of air-quality sensors situated around a city. There are 100 sensors located
- For the Petri net shown in Figure 4.18, identify all possible transitions that would cause the Petri net to be in a dead state, that is, no further transitions are possible. PA P2 Figure 4.18 Petri
- Why is it that there is no one, universally accepted strategy for software design modeling?
- Who should you write the design specification?
- What are the differences between object-oriented modeling and using data flow diagrams?
- For each of the following systems(a) Inertial measurement unit(b) Nuclear monitoring system(c) Airline reservations system(d) Pasta sauce bottling system what design approach would you use?
- Which of the languages discussed in this chapter provide for some sort of goto statement? Does the goto statement affect performance? If so, how?
- What other compiler options are available for your compiler and what do they do?
- Compare how Ada95 and Java handle the goto statement. What does this indicate about the design principles or philosophy of each language?
- Discuss the possibility of an “n-address” machine, where n > 3.
- The instruction set of a certain processor does not have the JLE, JLT, JGE (jump less equal, less than, and greater or equal), and JGT instructions. Assume the process does not have all other
- Describe the relationship between the main processor and coprocessor in a system with which you are familiar or one that you discover through Web research.
- Should the instruction following the TEST instruction be interruptible? If so, what must the implicit BRANCH instruction (interrupt) do?
- Microcoded computers tend to be superior to 1-, 2-, or 3- address computers with respect to overall performance. Why?
- What is the difference between coprocessing and multiprocessing? What are the advantages and disadvantages of each?
- GCP, Inc., has contracted you to analyze and develop commercial off-the-shelf (COTS) processors to be phased into their existing product lines. Your objective is to select four popular commercial
- It seems that there are far fewer commercial implementations of SIMD, MIMD, and MISD architectures than there were just 10 years ago. This is probably due to a variety of factors, including high
- What would be the appropriate operating system architecture for the:(a) Inertial measurement system(b) Nuclear monitoring system(c) Patient monitoring system(d) Airline reservations system(e) Pasta
- Should a task be allowed to interrupt itself? If it does, what does this mean?
- Discuss some of the advantages of EDF scheduling over RM scheduling and vice versa.
- Show with an example that EDF is no longer an optimal scheduling policy if preemption is not allowed.
- The following system of periodic tasks is scheduled and executed according to a cyclic schedule. Draw an execution trace (timeline) showing two occurances of each task. Ti ei Pi 1 8 T2 4 15 T3 3
- Consider the following tasks with their resource requirements given as:a) τ1 = (10, 4, 1; [A; 1]), where the task executes for two time units, then requests the resource A.(b) τ2 = (7, 4, 2; [A;
- For a machine you are familiar with, discuss whether the counting semaphore implementation given in this chapter has any critical-region problems. That is, can the semaphore itself be interrupted in
- Why is it not wise to disable interrupts before the while statement in the binary semaphore, P(S)?
- Discuss the problems that can arise if the test and set in the P(S) operation are not atomic. What could happen if the simple assignment statement in the V(S) operation were not atomic?
- Rewrite the save and restore routines assuming that eight general register (R0–R7) and the program counter are to be saved on a stack. Do this for(a) 0-address machine(b) 1-address machine(c)
- Rewrite the save and restore routines so that they save and restore to the head and tail of a ring buffer, respectively.
- Rewrite the save and restore routines in 2-address code, assuming block move (BMOVE) and restore (BRESTORE) instructions are available. Make the necessary assumptions about the format of the
- Rewrite the save and restore routines in the language of your choice so that they employ the push and pop procedures.
- A real-time system has a fixed number of resources of types A, B, and C. There are five tasks in the system, and the maximum amount of resources A, B, and C needed for each task is known. Implement a
- Show how priority inheritance can cause deadlock and also multiple blocking. For example, consider the following sequence (with τ1 τ2):τ1: Lock S1; Lock S2; Unlock S2; Unlock S1τ2: Lock S2; Lock
- Modify the write procedure for the ring buffer to handle the overflow condition.
- Consider a binary semaphore, counting semaphore, queues, and mailboxes. Any three can be implemented with the fourth. It was shown how binary semaphores can be used to implement counting semaphores
- The TANDS instruction can be used in a multiprocessing system to prevent simultaneous access to a global semaphore by two processors. The instruction is made indivisible by the CPU refusing to issue
- Obtain as much data as you can for as many of the existing commercial real-time systems as you can. Summarize your findings for each operating system, briefly, in narrative form.
- Use your selection criteria and the information you have obtained to create a matrix of features by-products. In other words, present the findings you describe in step 2 more succinctly in tabular
- For the following kinds of systems give your best recommendation as to the most likely commercial real-time operating system to use based on the selection criteria you developed(a) A controller
- In filter design you will be asked to use hyper-bolic functions. In this problem we relate these functions to sinusoids and obtain a definition of these functions so that we can actually plot
- Euler’s identity is very useful not only in obtaining the rectangular and polar forms of complex numbers, but in many other respects as we will explore in this problem.(a) Carefully plot x[n]
- Consider the complex function x(t) = (1 + jt)2 for − ∞ < t < ∞.(a) Find the real and the imaginary parts of x(t) and carefully plot them with MATLAB. Try to make MATLAB plot x(t)
- Consider complex numbers z = 1 +j, w = −1 + j, v = −1 − j, and u = 1 − j. You may use MATLAB compass to plot vectors corresponding to complex numbers to verify your analytic
- The exponential x(t) = eat for t ≥ 0 and zero otherwise is a very common continuous-time signal. Likewise, y(n) = αn for integers n ≥ 0 and zero otherwise is a very common discrete-time signal.
- Although sums behave like integrals, because of the discrete nature of sums one needs to be careful with the upper and lower limits more than in the integral case. To illustrate this consider the
- Suppose you wish to find the area under a signal x(t) using sums. You will need the following result found above(a) Consider first x(t) = t, 0 ≤ t ≤ 1, and zero otherwise. The area under
- Three laws in the computation of sums arefor any permutation p(k) of the set of integers kin the summation.(a) Explain why the above rules make sense when computing sums. To do that considerLet
- Find the ordinary differential equation relating a current source is(t) = cos(?0t) with the current iL(t) in an inductor, with inductance L = 1 Henry, connected in parallel with a resistor of R = 1?
- Another definition for the finite difference is the backward difference:∆1[x(nTs)] = x(nTs) − x((n − 1)Ts)(∆1[x(nTs)]/Ts approximates the derivative of x(t)).(a) Indicate how this new
- Let y(t) = dx(t)/dt, where x(t) = 4cos(2πt), − ∞ < t < ∞. Find y(t) analytically and determine a value of Ts for which ∆[x(nTs)]/Ts = y(nTs)(consider as possible values Ts = 0.01
- Consider a signal x(t) = 4cos(2πt) defined for − ∞ < t < ∞. For the following values of the sampling period Ts generate a discretetime signal x(n) = x(nTs) = x(t)∣t=nTs.(i) Ts =
- The geometric series
- To get an idea of the number of bits generated and processed by a digital system consider the following applications:(a) A compact disk (CD) is capable of storing 75 min of “CD quality”
- A phasor can be thought of as a vector, representing a complex number, rotating around the polar plane at a certain frequency in radians/second. The projection of such a vector onto the real axis
- Consider a function of z = 1 + j1, w = ez(a) Find (i) log(w), (ii) Re(w), (iii) Im(w)(b) What is w + w*, where w* is the complex conjugate of w?(c) Determine ∣w∣, ∠w, and ∣log(w)∣2?(d)
- Consider the following problems related to computation with complexnumbers.(a) Find and plot all roots of(i) z3 = − 1, (ii) z2 = 1
- Consider the calculation of roots of an equation zN = α where N ≥ 1 is an integer and α = ∣α∣ejφ a nonzero complex number.(a) First verify that there are exactly N roots for this
- Use Euler’s identity to(a) Show the identities(i) cos(α + β) = cos(α) cos(β) − sin(α) sin(β)(ii) sin(α + β) = sin(α) cos(β) + cos(α) sin(β)(b) Find an expression for cos(α)
- Use Euler?s identity in the following problems. (a)?Find trigonometric identities in terms of sin(?), sin(?), cos(?), cos(?) for (i) cos(? + ?) ? ? ?(ii) sin(? + ?) (b) Is it true that (c)?Is it
- Use Euler?s identity to (a)?show that (i) cos(? ? ?/2) = sin(?), (ii) ? sin(? ? ?/2) = cos(?), (iii) cos(?) = sin(? + ?/2). (b) to find (i) cos(2πt) sin(2π t)dt, (ii) cos, (2πt)dt
- Using the vectorial representation of complex numbers it is possible to get some interesting inequalities.(a) Is it true that for a complex number z = x + jy we have that ∣x∣ ≤ ∣z∣? Show it
- Consider the following problems about trigonometric and polar forms.(a) Let z = 6ejπ/4 find (i) Re(z), (ii) Im(z)(b) If z = 8 + j3 and v = 9 − j2, is it true that(i) Re(z) = 0.5(z + z∗)?
- Design an FIR low-pass filter with a cuttoff of π/3 and lengths N = 21 and N = 81,(a) Using a rectangular window(b) Using Hamming and Kaiser (β = 4.5) windows, and compare the magnitude of the
- Given the signals x[n] = 2n (u[n] − u[n − 3]) and y[n] = 0.5n (u[n] − u[n − 3]) write a matrix equation to compute their circular convolution of lengths N = 3, 4, and 5. Call the
- Consider an envelope detectorthat would be used to detect the message sent in an AM system. Consider the envelope detector as a system composed of the cascading of two sys-tems one which computes the
- A discrete-time system has a unit impulse response h[n].(a) Let the input to the discrete-time system be a pulse x[n] = u[n] − u[n − 4] compute the output of the system in terms of the
- An effect similar to multi-path in acoustics is echoing or reverberation. To see the effects of an echo in an acoustic signal consider the simulation of echoes on the handel.matsignal y[n]. Pretend
- Suppose we sample the analog signal x(t) = e?2t u(t), using a sample period Ts = 1 (a)?Expressing the sampled signal as x(nTs) = x[n] = ?n u[n], what is the corresponding value of ?? Use stemto plot
- The input of an LTI continuous-time system is x(t) = u(t) − u(t − 3.5). The system’s impulse response is h(t) = u(t) − u(t − 2.5).(a) Find the system’s output y(t) by graphically
- Determine the impulse response h[n] of a LTI system represented by the difference equation y[n] = ?0.5y[n ? 1] + x[n], where x[n] is the input, y[n] is the output, and the initial conditions are
- A two-bit quantizer has as input x(nTs) and as output x̂(nTs), ork∆ ≤ x(nTs) < (k + 1) ∆ → x̂(nTs) = k∆, k= − 2, − 1, 0, 1(a) Is this system time-invariant?
- For a finite-support signal x[n] = r[n](u[n] − u[n − 11]) where r[n] is the discrete-time ramp function,(a) Find the energy of x[n].(b) Find the even xe[n] and the odd xo[n] components
- Let x(t) = cos(? t)[u(t) ? u(t ? 2)] be the input of a zero-order hold sampler. The sampler samples every Ts sec starting at t = 0, and the impulse response of the zero-order hold is h(t) = u(t) ?
- Suppose we would like to send the two messages mi(t), i = 1, 2, created in Problem 16 using the same bandwidth and to recover them separately. To implement this consider the QAM approach where the
- The signal at the input of an AM receiver is u(t) = m1(t) cos(20t) + m2(t) cos(100t) where the messages mi(t), i = 1, 2 are the outputs of a low-pass Butterworth filter with inputs x1(t) = r(t) ?
- Design an analog low-pass filter satisfying the following magnitude specifications:αmax = 0.5 dB αmin = 20 dBΩp
- The specifications for a low-pass filter areα(0)=20 dBsΩp = 1500 rad/sec, α1 = 20.5 dBsΩs = 3500 rad/sec, α2 = 50
- Consider the transmission of a sinusoid x(t) = cos(2πf0t) through a channel affected by multipath and Doppler. Let there be two paths, and assume the sinusoid is being sent from a moving object so
- Control systems attempt to follow the reference signal at the input, but in many cases they cannot follow particular types of inputs. Let the system we are trying to control have a transfer function
- Suppose you would like to obtain a feedback implementation of an all-pass system with transfer function (a)?Determine the feedforward transfer function G(s) and the feedback transfer function H(s)
- An ideal operational amplifier circuit can be shown to be equivalent to a negative feedback system. (a)?Consider the inverting amplifier circuit and its two-port network equivalent shown in Figure
- Consider a filter with frequency response or a sinc function in frequency. (a) Find the impulse response h(t) of this filter. Plot it and indicate whether this filter is a causal system or not. (b)