Linearity implies two properties: additivity and homogeneity. We will first check the additivity of the system...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Linearity implies two properties: additivity and homogeneity. We will first check the additivity of the system y(t) = 2x(t). Create the Simulink diagram shown in Figure 9. You can find the "Gain" and "Sum" blocks from the "Math Operations" library. To copy a block, hold down the control key, left-click on the block and drag the copy to wherever it is needed. Make the amplitudes and frequencies of the two sine waves different. On the scope labeled "Additivity", the first waveform shows y(t) = 2(x, (t) + x₂ (t)) and the second one shows y₁(t) + y₂ (t), where y₁ (t) = 2x₁ (t), y₂ (t) = 2x₂ (t). Use different markers for these two signals to show that they do overlap. The third waveform is the difference of the first two, which shows zero for all time. Therefore, additivity is verified. Save the Simulink diagram for future use. 2 A Sine Wave x1(t) А Sine Wave x2(t) + 2 + 2 x1(t)+x2(t) y1(t)=2x1(t) y2(t)=2x2(t) 2 + 2(x1(t)+x2(t)) y1(t)+y2(t) + Additivity Figure 9 Verification of Additivity of the System y(t)=2x(t) Next, let's verify if it satisfies homogeneity. Create the Simulink diagram shown in Figure 10. (It is easier to modify Figure 9 than to start from scratch. Be sure to save under a new name.) Compare the waveform showing 2(Kx(t)) and the waveform showing Ky(t), for K = 3. The waveforms overlap and the difference is zero for all time. Homogeneity is verified. Again, use different markers to distinguish between signals. Save the Simulink diagram for future use. А Sine Wave x(t) 3 2 Kx(t) y(t)=2x(t) 2 3 2(Kx(t)) Ky(t) 1 Figure 10 Verification of Homogeneity of the System y(t)=2x(t) Homogeneity Now let's check if the system y(t) = 2x(t) is time-invariant. Create the Simulink diagram shown in Figure 11. Compare the two waveforms on Scope "Time Invariance" showing 2(x(t–T)) and y(t-T) respectively, where y(t) = 2x(t). The waveforms overlap and the difference is zero, for the same T in both "Transport Delay" blocks. Time-invariance is verified. Save the diagram for future use. A Sine Wave x(t) a x(t-T) 2 y(t)=2x(t) 2 2x(t-T) y(t-T) - + 1 Time Invariance DAC Figure 11 Verification of Time-invariance of the System y(t)=2x(t) Linearity implies two properties: additivity and homogeneity. We will first check the additivity of the system y(t) = 2x(t). Create the Simulink diagram shown in Figure 9. You can find the "Gain" and "Sum" blocks from the "Math Operations" library. To copy a block, hold down the control key, left-click on the block and drag the copy to wherever it is needed. Make the amplitudes and frequencies of the two sine waves different. On the scope labeled "Additivity", the first waveform shows y(t) = 2(x, (t) + x₂ (t)) and the second one shows y₁(t) + y₂ (t), where y₁ (t) = 2x₁ (t), y₂ (t) = 2x₂ (t). Use different markers for these two signals to show that they do overlap. The third waveform is the difference of the first two, which shows zero for all time. Therefore, additivity is verified. Save the Simulink diagram for future use. 2 A Sine Wave x1(t) А Sine Wave x2(t) + 2 + 2 x1(t)+x2(t) y1(t)=2x1(t) y2(t)=2x2(t) 2 + 2(x1(t)+x2(t)) y1(t)+y2(t) + Additivity Figure 9 Verification of Additivity of the System y(t)=2x(t) Next, let's verify if it satisfies homogeneity. Create the Simulink diagram shown in Figure 10. (It is easier to modify Figure 9 than to start from scratch. Be sure to save under a new name.) Compare the waveform showing 2(Kx(t)) and the waveform showing Ky(t), for K = 3. The waveforms overlap and the difference is zero for all time. Homogeneity is verified. Again, use different markers to distinguish between signals. Save the Simulink diagram for future use. А Sine Wave x(t) 3 2 Kx(t) y(t)=2x(t) 2 3 2(Kx(t)) Ky(t) 1 Figure 10 Verification of Homogeneity of the System y(t)=2x(t) Homogeneity Now let's check if the system y(t) = 2x(t) is time-invariant. Create the Simulink diagram shown in Figure 11. Compare the two waveforms on Scope "Time Invariance" showing 2(x(t–T)) and y(t-T) respectively, where y(t) = 2x(t). The waveforms overlap and the difference is zero, for the same T in both "Transport Delay" blocks. Time-invariance is verified. Save the diagram for future use. A Sine Wave x(t) a x(t-T) 2 y(t)=2x(t) 2 2x(t-T) y(t-T) - + 1 Time Invariance DAC Figure 11 Verification of Time-invariance of the System y(t)=2x(t)
Expert Answer:
Answer rating: 100% (QA)
It appears that youve provided detailed instructions for verifying the linearity and timeinvariance ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these medical sciences questions
-
What is the term for the practice of assigning funds to particular categories in order to cover expenses, handle outstanding debts, allocate resources for future objectives, or establish a financial...
-
You are the office manager and have received a letter from one of your patients, asking to know the names of all employees and care providers that have accessed their Electronic Health Record within...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
PERCH FALLS MINRO HOCKEY ASSOCIATION FUND Operating Capital Endowment Cash Inflows: Government grant for operating Costs $162 Government grant for hockey arena $350 Corporate donations for hockey...
-
Is there a number a such that Exists? If so, find the value of a and the value of the limit. 3x + ax + a + 3 x + x- 2 lim
-
Assume JKL corporation is considering increasing employees' monthly salary by 5% to help spur higher performance. Based on your regression analysis, how much of a difference, if any, do you predict...
-
Consider the all-possible-regressions analysis of the National Football League data in Problem 10.2. Identify the subset regression models that are \(R^{2}\) adequate (0.05). Data From Problem 10.2...
-
Cellular telephone service has certainly become more important vis--vis wired telephone service over the past decade. Will this trend continue? How will the trend toward cellular service be affected...
-
Blue Mountain Hardware is adding a new product line that will require an investment of $1,510,000. Managers estimate that this investment will have a 10-year life and generate net cash inflows of...
-
Suppose that fixed costs for a firm in the automobile industry (start-up costs of factories, capital equipment, and so on) are $5 billion and that variable costs are equal to $17,000 per finished...
-
2. Ws Gs = = n Yw Vs'Yw' Use the following phase relationships to answer the next two questions: W Ws y=/; d= Ysat = Ya ws 1 = V e = V Ws+Ww. Ww. Vw V Yw = Vw ST Ww. W = Ws Relationship required...
-
How is a firms marginal cost curve related to the market supply curve?
-
If the conditions for perfect competition are generally not met, why do economists use the model?
-
List three conditions for perfect competition.
-
Why must buyers and sellers be price takers for a market to be perfectly competitive?
-
Classify the following nudges as either a potentially advantageous default nudge, an information or encouragement nudge, or not a nudge. a. A firm redesigns its health enrollment form so that...
-
Longest Special Subsequences You are given a binary string S that contains only 0 and 1. Your task is to find the length of the longest special subsequence in string S. A special sequence is a binary...
-
Some people argue that the internal control requirements of the Sarbanes-Oxley Act (SOX) put U.S. companies at a competitive disadvantage to companies outside the United States. Discuss the...
-
Fisafolia Corporation has gross income from operations of $220,000 and operating expenses of $160,000 for 2012. The corporation also has $20,000 in dividends from publicly traded domestic...
-
Sherry rents her vacation home for 6 months and lives in it for 6 months during the year. Her gross rental income during the year is $4,000. Total real estate taxes for the home are $950, and...
-
Bill and Guilda each own 50 percent of the stock of Radiata Corporation, an S corporation. Guilda's basis in her stock is $25,000. On July 31, 2012, Bill sells his stock, with a basis of $40,000, to...
-
In problem 49, when does the estate's taxable year end? problem 49, John Henry died on May 1, 2018. When does his final 1040 have to be filed?
-
John Henry died on May 1, 2018. When does his final 1040 have to be filed?
-
John and Mary Hughes file their income tax return on a calendar year basis. John dies on May 15, 2018. Mary remarries on July 4, 2018. Can Mary file a joint return with John for the taxable year 2018?
Study smarter with the SolutionInn App