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Explore the intricacies of modeling and simulating sampled-data systems in this conference talk by Fredrik Bagge Carlson at JuliaCon 2024. Delve into the challenges of representing discrete computations in computers and their interactions with the environment. Examine examples of sampled-data systems, including control systems and digital signal-processing pipelines. Learn about complex engineering systems with multiple discrete-time partitions operating at different rates. Discover new capabilities in ModelingToolkit for handling mixed continuous-discrete systems, including the introduction of clocks, sample and hold operators, and code generation for discrete-time partitions. Gain insights into accurately analyzing and simulating complex sampled-data systems using Julia programming language tools.