Spring 2020 Assignment 8

From Course Wiki
Jump to: navigation, search
20.309: Biological Instrumentation and Measurement

ImageBar 774.jpg

Circuit analogies


Pencil.png

For each of the systems below, find an analogous circuit.


Convolution practice


Pencil.png

For each of the pairs of functions below, plot the convolution of the two functions, $ Y=A*B $


$ A $ $ B $ $ Y=A*B $
Delta(t+1)+delta(t-1).png Delta(t+1)+delta(t-1).png Bare convolution axes.png
Delta(t+1)+delta(t-1).png Box w=1.png Bare convolution axes.png
Delta(t+1)+delta(t-1).png Box w=2.png Bare convolution axes.png
Box w=1.png Box w=1.png Bare convolution axes.png
Delta(t+1)+delta(t-1).png Triangle.png Bare convolution axes.png
Delta(t).png Triangle.png Bare convolution axes.png


Fourier transform table

The two tables below show important properties of the Fourier transform and several useful transform pairs. You can use the tables of pairs and properties to figure out the transforms of an endless number of functions.


Pencil.png
  1. For each of the named functions in the Table of Common Functions and their Fourier Transforms, sketch the function in the time domain as well as the magnitude of its Fourier transform. Show relevant constants (for example: a, $ \alpha $, and $ f_0 $).
  2. Sketch the transform of $ \cos^4(\omega_0 t) $.
  3. Sketch the magnitude of the fourier transform of $ e^{-\alpha t} u(t) \times \cos(\omega_0 t) $. Assume $ \alpha\ll\omega_0 $.
  4. </div>


Short table of Fourier transform properties Short table of Fourier transform pairs

</div>
Retrieved from "http://measurebiology.org/w/index.php?title=Spring_2020_Assignment_8&oldid=44187"