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# HW3 - Hint Use what we have derived relating to the savings...

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EE 3120 Summer 2004 Homework 3 Assigned: Friday, June,25 Due: Thursday, July 1 Do not write on this sheet and turn it in. Do all work on other engineering paper. 1. Solve for the output y[k] give the input u[k] and the impulse response h[k]. 2. Find the first 5 terms y[k] using the following difference equation. First find the impulse response, then zero input response, then the zero state response, then the total response. Does the total response equal the sum of the zero state and zero input response? What does this say about the system? [ 2] 3 [ 1] 2 [ ] [ 2] 3 [ 1] 3 [ ] [ ] (3) [ ], [ 1] 3, and [ 2] 2 k y k y k y k u k u k u k u k q k y y + + + + = + + + + = - = - = What is the order of this equation? Is this equation recursive or nonrecursive? Is it the advanced or delayed form? 3. We wish to accumulate \$1,000,000 in retirement savings over the course of our working years (assume from ages 23 to 65, or 42 years). If the average interest rate on our earnings is 6% per year over those 42 years, how much money would we need to invest each year in our retirement?
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Unformatted text preview: Hint: Use what we have derived relating to the savings account example to find the answer. 4. If we assume that we will live until we are 85 (20 years after we retire). How much money can we withdraw (in one lump sum each year) from our \$1,000,000 retirement nest egg, assuming the money left in the retirement account will earn 5% per year. Hint: This is similar to the equal payment mortgage example. 5. Execute a the convolution of the following two sequences using: a. Direct solution of the convolution summation b. Using the tabular method c. Using the graphical method. 1 2 [ ] [1,0, 4,2,5, 2], [ ] [2, 2,1, 1,0,0] f k f k =--=--6. Find the convolution of the following functions. Use any one method you prefer. a. [ ] [ ] [ ] y k q k k δ = b. [ ] sin[ ] [ ] 2 y k k k π = c. [ ] [ ] [ 5] y k q k k =-d. [ ] [ ] [ ] y k q k q k = e. 3 [ ] [ 2] [ ] y k q k p k = + f. 3 3 [ ] [ ] [ ] y k p k p k = g. 2 4 [ ] [ ] [ ] y k p k p k = h. [ ] [ ] [ ] y k r k r k =...
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