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Digital Filtering and Exact Reconstruction of Digital Audio

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Introduction This elaborates some of the claims in my insights article on digital audio. The Sinc Function The first link in my insights article has a section on filters, but I will detail the most critical case. The bit depth is assumed to be so large for all practical purposes that it is infinite, and…

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Introduction to Modern Digital Audio Concepts

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Introduction First, we need some background in Digital Signals. This can be mathematically quite advanced, but since I would like this article to be accessible to as wide an audience as possible, here is a link that explains what is needed (not even Calculus is required): https://brianmcfee.net/dstbook-site/content/intro.html An important point not emphasized in the above…

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Differential Equation Systems and Nature

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Abstract “Mathematics is the native language of nature.” is a phrase that is often used when it comes to explaining why mathematics is all around in natural sciences, especially in physics. What does that mean? A closer look shows us that it primarily means that we describe nature by differential equations, a lot of differential…

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Why ChatGPT AI Is Not Reliable

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I’ll start with the simple fact: ChatGPT is not a reliable answerer to questions. To try to explain why from scratch would be a heavy lift, but fortunately, Stephen Wolfram has already done the heavy lifting for us in his article, “What is ChatGPT Doing… and Why Does It Work?” [1] In a PF thread…

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Programming an ATmega8A using Arduino

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If you are interested in programming and electronics, you probably do not need an introduction to Arduino. If you want to make your Arduino projects permanent, then it is a good idea to use solo microcontrollers rather than Arduino boards in the final setup. While Arduino boards are great for prototyping, buying an Arduino board…

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P vs. NP and what is a Turing Machine (TM)?

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P or NP This article deals with the complexity of calculations and in particular the meaning of ##P\stackrel{?}{\neq}NP## Before we explain what P and NP actually are, we have to solve a far bigger problem: What is a calculation? And how do we measure its complexity? Many people might answer, that a calculation is an…

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Quantum Computing for Beginners

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This article provides an accessible introduction to quantum computing, a cutting-edge technology that processes certain types of information much faster than conventional computers. Major companies like Google, Microsoft, IBM, and Intel are heavily investing in its development due to its potential to solve complex problems that are currently infeasible for classical computers, such as creating…

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Parallel Programming on a CPU with AVX-512

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This article is the second of a two-part series that presents two distinctly different approaches to parallel programming. In the two articles, I use different approaches to solve the same problem: finding the best-fitting line (or regression line) for a set of points. The two different approaches to parallel programming presented in this and the…

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Parallel Programming on an NVIDIA GPU

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This article is the first of a two-part series that presents two distinctly different approaches to parallel programming. In the two articles, I use different approaches to solve the same problem: finding the best-fitting line (or regression line) for a set of points. The two different approaches to parallel programming presented in this and the…

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