Reference no: EM13764786
1. Express the numbers in Cartesian (rectangular) form.
2. Express the following numbers in polar form. Describe the quadrant of the complex plane, in which the complex number is located.
(a) 1 + j1
(b) 1 - j1
(c) -1 + j1
(d) -1 - j1
3. (a) A continuous-time sine wave has a frequency of 60 Hz, an amplitude of 117 V, and an initial phase of π/4 radians. Describe this signal in a mathematical form using the Sin function.
(b) Determine the period of the signal. Be sure to mention the units of the period.
(c) Describe this signal in a complex exponential form
4. A sinusoidal signal described by 50 Cos (20πt + π/4) passes through a linear time invariant (LTI) system that applies a gain of 1.5 and a phase lag of π/2 radians to the signal. Write the mathematical expression that describes the signal that will come out of the LTI system.
5. A sinusoidal signal described by 20 Cos (2πt + π/4) passes through a linear time invariant (LTI) system that applies a gain of 2 and a time delay of 0.125 seconds to the signal. Write the mathematical expression that describes the signal that will come out of the LTI system.
6. Apply the principle of superposition to determine whether the following systems are linear. Sketch what the plot of the function looks like.
(a) Y = 5x + 1
(b) Y = 5x
(c) Y = 5X2
7. A continuous time system, described by y(t) = 5 Cos (2*π*20*t + π/2), is sampled at a rate 320 Hz.
(a) Write the mathematical expression that describes the discrete time (sampled) signal.
(b) Calculate the value of the discrete signal for n = 0 and n = 4.
(c) Does the sampling rate meet the Nyquist condition? Justify your answer.
8. Sketch the odd and even part of the following discrete signal. (See pages 13-14 of the text.)
9. Express the signal given in Problem 8 as the sum of the following.
(a) Delayed and undelayed (if any) impulses
(b) Delayed and undelayed (if any) step functions.
What major challenges or barriers exist
: How would you recommend a strategy to repair or replace the various aging critical infrastructure? Explain. What major challenges or barriers exist? Explain
|
Identify what strategic leadership skills
: Identify what strategic leadership skills are needed for your entrepreneurial venture to take it to the next growth level. How will you evaluate the leaders in your venture to etermine if they have thestrategic leadership skills needed?
|
What qualities do you personally prefer in a strong leader
: What qualities do you personally prefer in a strong leader, and why do you think these are meritorious. Be specific in your description and rationale
|
Prepare a multistep income statement
: On a spreadsheet, prepare a multistep Income Statement for the year ending 12/31/12 with proper heading. See link below for sample income statement. Near the bottom of your income statement should have a subtotal for Income before taxes and then s..
|
Determine the period of the signal
: Determine the period of the signal. Be sure to mention the units of the period. Describe this signal in a complex exponential form
|
Difference between accounting costs and economic costs
: If the revenue a firm receives is more than the firm's direct costs, but is less than the firm's total costs including all opportunity costs, the firm is experiencing.
|
Theory and practices of law enforcement
: Community Information: In this section you will want to include the size and location of the community, and any major issues. BCJ 2001, Theory and Practices of Law Enforcement
|
How one of literary elements contributes to power of work
: how one of the literary elements contributes to the power of the work. You will need to be specific, so you are certainly welcome to focus on a specific episode or even a certain line of a song.
|
Reported an ending inventory balance
: On December 31 of the current year, Hewett Company reported an ending inventory balance of $216,500. The following additional information is also available:
|