Foundational — DSP Notes: RF Spectrum Bands and Applications

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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

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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

Developmental – Welcoming The Gamma Function

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"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)

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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)

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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)

Developmental – DMD Meets Space City (Part I)

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Imagine being able to detect subtle patterns in Earth's landscape using mathematical tools. With NASA's API for obtaining LANDSAT Imagery and the Dynamic Mode Decomposition (DMD) technique, this becomes not only possible but accessible to anyone with enough curiosity and a reasonable understanding of python. Here are the highlights: LANDSAT Summary Accessing NASA's API DMD … Continue reading Developmental – DMD Meets Space City (Part I)

Developmental – What About Those Pesky Integrals?

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So what about those pesky definite integrals? I mean the ones integrating over a high number of dimensions. Many ML problems, especially in Bayesian statistics, involve computing probabilities or expectations over high-dimensional spaces. For this reason, we're gonna need a clever way to compute these integrals. Enter Monte Carlo Integration! This technique isn't just a … Continue reading Developmental – What About Those Pesky Integrals?