Abstract
In this experiment, we compared the frequency domain representation of several periodic signals to predictions based on Fourier Series. We performed a Fast Fourier Transform on periodic signals using an application in LabView. Our results _____________ correspond with the theoretical predictions, but our measurements for _______________ differed from the predictions due to __________________________. The widest bandwidth we measured was for the _____________________________ signal, and this was __________ times the fundamental frequency. We found that adding a DC offset _____________ affect the frequency domain representation. Changing the signal amplitude or frequency of the periodic waveform caused a ________________________ in the amplitudes or frequencies of the frequency domain representation. We also measured the effective and absolute bandwidth of a square pulse, and found that the effective bandwidth was _______ times the inverse of pulse duration, and the absolute bandwidth was _______ times the pulse duration.
Introduction
In this lab, we learned a great deal about using the equipment in the laboratory. We used the Digital Oscilloscope to verify that all waveforms were properly generated, with the correct amplitude and duty cycle. We used two types of virtual instruments in LabView, a spectrum analyzer and a pulse analyzer. These instruments automatically calculated the DC Offset, power, effective bandwidth, and Cheez WhizÒ content of these waveforms. We measured the amplitude of each peak in the spectrum up to 8 times the fundamental frequency. (Put here anything you want to add that describes the lab, without worrying about brevity as you do for the abstract.)
Theory
Include the theory pages from the lab book, or write your own theory section that covers this material and any other material you feel is needed..
Equipment
Include the equipment page from the lab book, or write all the equipment information in this section.
Method
Include the method pages from the lab book, or enter the method here. If entering the method, you do not have to re-draw the connection diagrams, and you do not have to repeat it verbatim, but it must accurately reflect the experiment procedure.
Results
Prior to the lab, you must have all theoretical predictions in the "Raw Data and Error Estimates" part of the lab handout completely filled out. During the lab, you must use these pages to fill in the results, error estimates, and error calculations for each measurement. Do not change anything on these sheets after you have left the lab.
Before you leave the lab, be sure that the error of all your measurements falls within the span of your error allowance. If it does not, either redo that part of the lab or determine the source of the additional error in your experiment.
You can submit your original pages directly in your lab report. If there is an easily correctible mistake in your data or error estimates (a misplaced decimal point, a missed digit, or an inverted sign), do not correct the original pages, but write a paragraph in the results section explaining the mistake and how you corrected it. If there are more extensive problems with your data or error estimates, you should address them in the error analysis or discussion section.
You may print your results in tables that you create for your lab report. If you create tables, make sure you present only the original data and error estimates (write a paragraph about simple corrections if necessary). Submit the original data pages which you used during the lab as an appendix to your lab report.
You may also rewrite your results on a new copy of the "Raw Data and Error Estimates" pages of the lab handout (with handwritten notes about simple corrections). You must also submit your original data pages as an appendix to your lab report.
You can download the results pages of the lab handout (Microsoft® Word format) from the class website: http://www.cs.ucla.edu/classes/cs171L .
Observations
Here you can express anything interesting you saw that is not quantitative. If there was something during the lab that you think might have impacted your results (even if you are not sure exactly how) express it here. If you had trouble with the lab equipment, or if you think the equipment might have been faulty, express that here also.
If your observations are about additional sources of error that may have caused your results to exceed the error allowance, you must discuss these sources of error in the error analysis section. If you made observations about possible sources of error that did not cause your results to exceed the error allowance, you can just mention them here.
Error Analysis
Here you should describe the calculations of error allowance that you performed in the "Results and Error Estimates" section of the lab handout. List the sources of error in each part of the experiment. If the error of any measurement is greater than the error allowance, you must discuss what additional sources of error were present (or whether some source of error may have been stronger than you estimated).
For the bandwidth calculations, don’t take a percentage error, but discuss any discrepancies between the theory and your results. What could cause the result to be different than the expected? There’s no percentage error you can easily calculate, but you still need to address error in the bandwidth measurement part of this lab.
Similarly, for the solitary pulse, discuss any discrepancies between the theory (effective bandwidth = 0.27 x 1/pulse width, absolute bandwidth 4.5 x 1/pulse width) and your results. Again, there’s no percentage error you can easily calculate, but you still need to address error in this part of the lab.
Discussion
Discuss each part of the lab report. It might be a good idea to put a separate paragraph for each part with the name of that part. For instance:
Part A
The sinusoidal frequency domain representation was composed of only one peak at the same frequency as the sinusoidal waveform. et cetera
Be sure to ANSWER ALL QUESTIONS in the lab report. If you have trouble understanding the questions, or don’t feel you can answer them based on your knowledge, contact the TA. If you can’t reach the TA, answer the question to the best extent of your knowledge, but include some kind of answer in your report.
Conclusion
Include anything else here you want to say about the lab. If you want to comment about anything in the lab, or suggest ways to improve the lab, please mention them here. This section is an extension of the discussion, so if there’s something you want to include that you think doesn’t belong in the discussion (but you’re not absolutely sure), put it here.
Appendix
Include the spectrum analyzer printouts for all measurements of this lab. Also include the original results pages which you filled out in the lab. Do not change anything on these sheets after you have left the lab; if there are corrections, print out a new copy of the results pages and submit them as the "Results" section. make your corrections on these pages. If you believe there are significant problems with the data that the TA did not catch before you left the lab, discuss this with the TA. Also include ALL spectrum analyzer printouts. Label each printout according to the specific part of the lab.