I see that you've uploaded an image with several problems related to signals and systems, Fourier transforms, and linear time-invariant (LTI) systems. I'll help you solve or guide you through one of the questions in detail. Let me break down the problems:

1. Problem 1: Deals with the periodicity and invertibility of systems and finding their inverse.

   • (a) Checking periodicity of signals and finding their fundamental periods.
   • (b) Checking if systems are invertible and, if so, finding their inverse.
   • (c) Finding the response of an LTI system.

2. Problem 2: Is centered around Fourier series representations and LTI systems.

   • (a) Fourier series representation of a periodic signal $x(t)$.
   • (b) Finding the Fourier series representation for the output $y[n]$ given a causal discrete-time LTI system.
   • (c) Finding Fourier series coefficients for an LTI system given an input.

3. Problem 3: Involves finding the Fourier transforms of certain signals.

Would you like help with a specific part of this question set, or should I solve them in sequence starting from Problem 1?

Let me know if you'd like to focus on a specific question!