Find All

The questions below are due on Thursday February 27, 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.

Consider the following signals:

  • f_1[n]={1\over2}+6\cos(\pi n/2)+4\cos(\pi n/5-\pi/2)
  • f_2[n]=\cos(1.8\pi n)+2\sin(2.7\pi n)
  • f_3[n]=\Big|\sin(\pi n/10)\Big|; where \big|x\big| represents the magnitude of x
  • f_4[n]=\mbox{Im}\Big\{e^{j\big(2\pi n/20+\pi/2\big)}\Big\}; where Im\{x\} represents the imaginary part x

Part a. Determine which (if any) of signals f_1[n] through f_4[n] are symmetric about n{=}0. Briefly explain.

Part b. Determine which (if any) of signals f_1[n] through f_4[n] are periodic with a fundamental (smallest) period N{=}20. Briefly explain.

Part c. Determine which (if any) of signals f_1[n] through f_4[n] can be represented by Fourier series with purely imaginary coefficients. Briefly explain.

Part d. Determine which (if any) of signals f_i[n] can be represented by Fourier series coefficients F_i[k] that are symmetric functions of k (i.e., F_i[k]=F_i[-k]). Briefly explain.

Please upload a single pdf file that contains your answers to all parts of this problem:

 No file selected