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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!

Find the Fourier series representation, check periodicity and invertibility of systems, and solve for Fourier transforms based on the provided signals and LTI systems.

Explore detailed solutions for Fourier series representation, system invertibility, periodicity of signals, and Fourier transforms involving discrete-time LTI systems. Suitable for college-level students studying signal processing.

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