Archive for the Category: Mathematics

Using Companion Models for Time-Domain Simulation of ODE’s

Companion models can be used to quickly formulate the solution of simultaneous ordinary differential equations like those associated with analog circuitry. This approach is particularly helpful when this capability must be embedded in tools like MATLAB / SIMULINK / C++. The PDF file is located by following this link.

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Updated Filter Design Documentation

Major revision to my filter design documentation 5.74 MB

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Approximation for RMS

Approximation for SQRT( I2 + Q2 ) with Gaussian Noise Present When a complex signal is represented in terms of in-phase (I) and quadrature-phase (Q) components, a commonly used approximation for the signal root-mean-square (RMS) value is Assuming a large number of OFDM subcarriers in the intended application, I and Q appear to both be […]

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Computing Data Windows Recursively

Data windows are indispensable for computing the spectral characteristics of signal waveforms that are not periodic in time. In the context of hardware-based digital signal processing, most if not all data windows are expressed in terms of fairly complex function that are not convenient for embedding in a FPGA or custom ASIC. This memo presents […]

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Dreaded Interview Questions Just for Fun- Part I

James A Crawford Having reached a sufficient station in life that I have either heard most of the typical interview questions that might come my own direction, or have the wit and nonsense to navigate my way through something that I don’t know and talk about the weather or something completely unrelated, this on-going collection […]

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Digital Re-Design of Analog Phase-Locked Loops

Abstract The need frequently arises to design a discrete-time digital signal processing (DSP) algorithm that closely mimics a conventional continuous-time phase-locked loop (CTPLL). Similarly, it is often desirable to talk about the DSP implementation in terms of traditional quantities like damping factor and equivalent noise bandwidth. This memorandum examines this interplay between discrete and continuous […]

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Pendulum & Elliptic Integrals

Many years ago before the advent of the “PC on every desktop” age, I became fascinated with the design of LC elliptic filters. As part of that endeavor, I also became intimately acquainted with elliptic integrals. Having an equal intrigue for numerical precision, I found that computing the elliptic integrals with high accuracy was very […]

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