Hermite-Hadamard Type Inequalities and Convex Functions in Signal Processing

This article explores the integration of HermiteHadamard Type Inequalities and convex functions within the domain of signal processing, elucidating their theoretical underpinnings and practical implications. Beginning with a comprehensive background, we focus on the historical context and foundational concepts that underlie these mathematical constructs. Our discussion progresses to articulate the problem formulation, delineating the specific challenges and objectives addressed in the study. The theoretical framework elucidates the HermiteHadamard Type Inequalities, highlighting their mathematical formulations, properties, and fundamental proofs. Concurrently, the discourse unfolds the theory and properties of convex functions, elucidating their significance and applications within signal processing paradigms. With a focus on applications, we illustrate the utility of Hermite-Hadamard Type Inequalities and convex functions in signal processing tasks. Through empirical studies and case examples, we demonstrate their efficacy in signal denoising, compression, and feature extraction, showcasing tangible results and comparative analyses. We discuss the challenges and limitations inherent in the application of these mathematical constructs in real-world scenarios, thereby paving the way for future research directions and advancements. Finally, we conclude by summarizing the key insights gleaned from our exploration and underscore the profound implications of Hermite-Hadamard Type Inequalities and convex functions in shaping the landscape of contemporary signal processing methodologies.