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Foundational — DSP Notes: On Discrete Sequences and Systems (Part I)
"Learning digital signal processing is not something you accomplish; it's a journey you take."-- Richard G. Lyons Our last post (article III) covered radio frequency spectrum bands and their applications. However, the primary reason for starting this series is to develop both theoretical and practical knowledge of DSP. Over time, readers can expect an Applied … Continue reading Foundational — DSP Notes: On Discrete Sequences and Systems (Part I)
Foundational — DSP Notes: RF Spectrum Bands and Applications
So far we have established several mathematical cornerstones of DSP. Particularly in articles I and II, we covered complex numbers, the closed-form of geometric series, logarithms, and metric prefixes. Now we'll turn our attention to another foundational pillar of this study: developing an intuition for frequency, as well as understanding the Radio Frequency Spectrum bands … Continue reading Foundational — DSP Notes: RF Spectrum Bands and Applications
Advanced –A Treatise on Parametric Forms of Multimodal Distributions
This document is part of a developing theoretical framework authored by Christopher Lee Burgess. Abstract Classical variance is insufficient for characterizing the geometric structure of multimodal data. In this work, we will define a new quantity called the pseudovariance, and demonstrate how it captures shape, modality, and dispersion through a general class of functions we … Continue reading Advanced –A Treatise on Parametric Forms of Multimodal Distributions
Protected: Advanced – Symmetries Reimagined (Part Two Draft)
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Developmental – Welcoming The Gamma Function
"The art of doing mathematics consists in finding that special case which contains all germs of generality." -- David Hilbert. The Gamma function appears in many areas of mathematics, physics, and engineering. This post will not only provide motivation for studying the Gamma function but also present several methods for deriving it, including an introduction … Continue reading Developmental – Welcoming The Gamma Function
Foundational – DSP NOTES: MATH OVERVIEW (PART II)
In Part I of our DSP Math Overview, we covered complex numbers and the closed-form solution for geometric series. Now, we will turn our attention to logarithms, their properties, and metric prefixes. Logarithms I'd like to begin part two of the math review with a section on logarithms and their properties. We will also cover … Continue reading Foundational – DSP NOTES: MATH OVERVIEW (PART II)
Foundational – DSP Notes: Math Overview (Part I)
Every image you see, every song you stream, every signal being transmitted across space… at its core, it's all just numbers. Digital Signal Processing (DSP) is a silent architect of modern technology, with widespread Industrial and Scientific applications. This series was inspired by a conversation I had with my brilliant friend Rose, motivating us to … Continue reading Foundational – DSP Notes: Math Overview (Part I)
OPERATION GRADIENT: MY 15A EXPERIENCE (PART II)
During the course, my instructors emphasized discretion regarding the syllabus and post-graduation details. As a result, my Operation Gradient blog posts will not delve into the specific course structure or provide a comprehensive summary of everything covered. Instead, these blog posts will form a coup d'œil (or glimpse) referring to shared moments of inspiration, memorable … Continue reading OPERATION GRADIENT: MY 15A EXPERIENCE (PART II)
OPERATION GRADIENT: MY 15A EXPERIENCE (Part I)
What is a gradient? Many students plowing their way through Calculus III can readily answer this question. In fact I would have, before attending the esteemed Operations Research Analyst course (15A) for incoming officers in the US Air Force. Now I consider this question as much philosophically as I do mathematically, especially in terms of … Continue reading OPERATION GRADIENT: MY 15A EXPERIENCE (Part I)
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