Midterm

1. Determine Laplace transform of .
2. Determine if y(t)=cos(x(t)) is linear, time-invariant, and/or causal.
3. Determine if is periodic; if periodic, calculate the period.
4. Compute the inverse Laplace transform of .
5. For the circuit shown below, find the input/output differential equation.

Lab5 – The Fourier Series and Fourier Transform

• Watch video entitled “Module 5 – Fourier Transform in MATLAB”

• Perform activity 1 below for the lab assignment using MATLAB.
• Include answers for Problems and include MATLAB coding along with any output plots that support solutions into a Word document entitled “Lab5_StudentID”.  Where your student id is substituted in the file name.

• Upload file “Lab5_StudentID”.

Activity 1:

A continuous time function is shown below in figure 1.  This signal is a sinc function defined as y(t) = sinc(t).  The Fourier transform of this signal is a rectangle function. 

1. Use the function linspace to create a vector of time values from -5 ≤ t ≤ 5.  Next, plot the function shown in figure 1 using the sinc function for y(t) = sinc(t).
2. Using Matlab and the command fft, show that the Fourier transform pair is indeed a rectangle function.  Use the command fftshift to center your plot.  Don’t forget that the Fourier transform is complex, with both magnitude and phase.    Your result should be the same as figure 2.  Show both your m-file code and plot.

Matlab tip:  The following commands are useful when working with the Fourier transform:

abs gives the magnitude of a complex number (or absolute value of a real number)

angle gives the angle of a complex number, in radians

[Note:  The fft command does not give the exact transform for a continuous time signal, which we have in this case.  For instance, the magnitude will not be correct.  However, in order to obtain the general shape including relative magnitudes, it can be quite useful.]

1. Using the same time values, plot the continuous time function defined as y(t) = sinc(2t).
2. Plot the transform pair for this signal.

Questions:

1. What is the cause of the “ringing” seen on top of the rectangular pulse shown in figure 2?
2. In step 3 above, the sinc function gets compressed by a factor of 2, as seen by comparing the graphs in the time domain.  What happened to the rectangular pulse in the frequency domain?  What property does this represent?

Figure 1

Figure 2

HW5 – The Fourier Transform

• Read Chapters 5 and section 8.2.5 in the text Signals and Systems Using MATLAB.

• Download and review the supplemental questions.
• Work the below five homework problems.
• Submit homework solutions via Assignment Upload Tool.  Show all work for full credit.

1. A continuous time signal x(t) has the Fourier transform  where b is a constant.  Determine the Fourier transform for .
2. A continuous time signal x(t) has the Fourier transform  where b is a constant.  Determine the Fourier transform for
3. Compute the Fourier transform for
4. Compute the inverse Fourier transform for
5. A signal with the highest frequency component at 10 kHz is to be sampled.  To reconstruct the signal, the sampling must be done at a minimum frequency of?

Chapter 1 and its appendix discuss the importance of managerial accounting and corporate governance.  Ethics are an integral part of both processes.

Research briefly an accounting scandal (make sure another student has not already covered it) and reply in the “followup discussions” section below (“Start a new followup discussion”) with the following items:

• Company name
• Time period of fraud
• How the fraud was committed
• How the fraud was discovered
• What were the results for the company and individuals involved (punishments, bankruptcy, etc.)
• What could have been done to prevent the fraud

Be sure to cite any sources you used.  Your response should be 1-2 paragraphs.

Caterpillar is the world’s leading maker of earth- moving machinery and supplier of agricultural equipment. The software for its Dealer Business System (DBS), which it licenses to its dealers to help them run their businesses, is becoming outdated. Senior management wants its dealers to use a hosted version of the software supported by Accenture Consultants so Caterpillar can concentrate on its core business. The system had become a defacto standard for doing business with the company. The majority of the 50 Cat dealers in North America use some version of DBS, as does about half of the 200 or so Cat dealers in the rest of the world. Before Caterpillar turns the product over to Accenture, what factors, and issues, should it consider? What questions should it ask? What questions should its dealers ask? Make a recommendation to senior management about preventing possible barriers for full implementation and acceptance of the new system.

(1) Your outline should state with your title page.

(2) List your your References section the three academic resources (peer-reviewed) for the paper.