Assignment 8, Part 0: convolution practice
The following two tables will pop up frequently in 20.309 for the rest of the semester. Table 8.0.1 describes the Fourier transform and many of its useful properties, while table 8.0.2 contains the transform pairs of many common functions. These two tables are useful because you can combine functions in table 8.0.2 using the properties in table 8.0.1 to figure out the transforms of an endless number of functions (without doing any math!).
Note: there is an error in the table for the transform of $ u(t) $. The correct transform is: $ \pi \delta(omega) + \frac{1}{j omega}. [[Image: FourierTransformsTable.png|thumb|left|500 px|<caption>Table 8.0.1: Short table of Fourier transform properties</caption>]] [[Image: TimeFrequencyDomains_MoreTransformPairsTable.png|thumb|left|500 px|<caption>Table 8.0.2: Short table of Fourier transform pairs</caption>]] {{Template:Assignment Turn In|message= <ol type="A"> <li>Sketch each function in table 8.0.2 as well as the magnitude of its Fourier transform. Include any relevant constants in your sketch (for example: ''a'', <math>\alpha $, and $ f_0 $).
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Some of the frequency plots are shown on log-log axes and some are linear, as indicated by the plot title.
Hint: Gaussian or white noise is a random signal with equal contributions from every frequency.
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- Overview
- Part 1: feedback systems
- Part 2: fabricate a microfluidic device
- Part 3: add flow control and test your device
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