Difference between revisions of "Assignment 8, Part 0: convolution practice"
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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!). | 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 <math>u(t)</math>. The correct transform is: <math>\pi \delta(omega) + \frac{1}{j omega}. | + | Note: there is an error in the table for the transform of <math>u(t)</math>. The correct transform is: <math>\pi \delta(omega) + \frac{1}{j omega}</math>. |
[[Image: FourierTransformsTable.png|thumb|left|500 px|<caption>Table 8.0.1: Short table of Fourier transform properties</caption>]] | [[Image: FourierTransformsTable.png|thumb|left|500 px|<caption>Table 8.0.1: Short table of Fourier transform properties</caption>]] |
Revision as of 17:39, 13 October 2022
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} $.
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- Part 1: feedback systems
- Part 2: fabricate a microfluidic device
- Part 3: add flow control and test your device
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