Fourier Series Transformations

The questions below are due on Thursday September 18, 2025; 02:00:00 PM.
 
You are not logged in.

Please Log In for full access to the web site.
Note that this link will take you to an external site (https://shimmer.mit.edu) to authenticate, and then you will be redirected back to this page.

Part a. Let f_1(t) represent the following periodic, continuous-time signal, with period T=1:

Let g_1(t)=1-f_1\big(3t{-}{1\over4}\big).

Sketch g_1(t) on the following axes. Label the important parameters of your plot.

Part b. Let f_2(t) represent the following periodic, continuous-time signal with period T=1:

Let g_2(t)=1-f_2\big(3t{-}{1\over4}\big).

Let F_2[k] and G_2[k] represent the Fourier series coefficients for f_2(t) and g_2(t), respectively, where both series are computed with the same period T=1. Determine expressions for each of G_2[0] through G_2[15] in terms of the Fourier coeeficients F_2[k]. Your table entries can contain real and/or imaginary numbers and constants such as e and \pi. Your entries should not contain integrals or infinite sums.


Upload your solution to this problem (including parts a, b, and c) as a single pdf file.
Your most recent submission before the problem deadline is the one that will be graded.
 No file selected