Difference between revisions of "Spring 2020 Assignment 8"
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{{Template: 20.309}} | {{Template: 20.309}} | ||
+ | ==Convolution practice== | ||
+ | {{Template:Assignment Turn In|message= | ||
+ | For each of the pairs of functions below, plot the convolution of the two functions, <math>Y=A*B</math> | ||
+ | }} | ||
+ | |||
+ | {| | ||
+ | !A | ||
+ | !B | ||
+ | !Y | ||
+ | |- | ||
+ | |[[File:delta(t+1)+delta(t-1).png]] | ||
+ | |[[File:delta(t+1)+delta(t-1).png]] | ||
+ | |[[File:bare convolution axes.png]] | ||
+ | |- | ||
+ | |[[File:delta(t+1)+delta(t-1).png]] | ||
+ | |[[File:box w=1.png]] | ||
+ | |[[File:bare convolution axes.png]] | ||
+ | |- | ||
+ | |[[File:delta(t+1)+delta(t-1).png]] | ||
+ | |[[File:box w=2.png]] | ||
+ | |[[File:bare convolution axes.png]] | ||
+ | |- | ||
+ | |[[File:box w=1.png]] | ||
+ | |[[File:box w=1.png]] | ||
+ | |[[File:bare convolution axes.png]] | ||
+ | |- | ||
+ | |[[File:delta(t+1)+delta(t-1).png]] | ||
+ | |[[File:triangle.png]] | ||
+ | |[[File:bare convolution axes.png]] | ||
+ | |- | ||
+ | |[[File:delta(t).png]] | ||
+ | |[[File:triangle.png]] | ||
+ | |[[File:bare convolution axes.png]] | ||
+ | |} | ||
+ | |||
==Circuit analogies== | ==Circuit analogies== | ||
{{Template:Assignment Turn In|message= | {{Template:Assignment Turn In|message= |
Revision as of 02:41, 23 April 2020
Convolution practice
For each of the pairs of functions below, plot the convolution of the two functions, $ Y=A*B $ |
A | B | Y |
---|---|---|
Circuit analogies
For each of the systems below, find an analogous circuit. |
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 below. The transform of $ u(t) $ is: $ \frac{1}{2}\left ( \frac{1}{i \pi f}+\delta (f) \right ) $.
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