Applied Fourier Analysis
From Signal Processing to Medical Imaging
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Article
Understanding the evolving phenotype of vascular complications in telomere biology disorders
Vascular complications such as bleeding due to gastrointestinal telangiectatic anomalies, pulmonary arteriovenous malformations, hepatopulmonary syndrome, and retinal vessel abnormalities are being reported in...
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Book
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Chapter
Basic Fourier Series
We will now study the basic rules of Fourier Series. You can study these basic principles for years in order to completely understand some of the many subtleties. The concentration of this book will be to quic...
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Chapter
The Fourier Transform
The transition from Fourier Series which were introduced in Chapter 2, to the Fourier Transform is similar to the transition from the dot product to the inner product. W...
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Chapter
Digital Communications
Digital communications are at the center of modern life. Cell phones have revolutionized the way we communicate. While they were scarcely available 20 years ago, it is very hard to imagine life without them to...
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Chapter
Image Processing
We have studied the use of the Fourier Transform on one-dimensional problems on a number of problems. Fourier Analysis is also extremely valuable as a tool to understand multidimensional problems. Modern cable...
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Chapter
Partial Differential Equations
Fourier Analysis is central to the study of a great number of physical phenomena. The periodic nature of vibrations and wave propagation are generally modeled by differential equations. We will study just a fe...
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Chapter
Introduction: From Linear Algebra to Linear Analysis
The subject of Fourier Analysis is at the center of many modern sciences. Physics and engineering depend so heavily on the subject, it is hard to imagine even mentioning them without thinking immediately about...
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Chapter
The Discrete Fourier Transform
Fourier Series is a way to represent a function \(f(t) \in L^2[a, b]\) f ...
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Chapter
Sampling and Interpolation
We will consider one of the most fundamental applications of Fourier analysis. If you turn on your stereo, listen to the radio, talk on your cell phone, or use the internet today, you will be utilizing the fun...
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Chapter
Radar Processing
Radar processing began in most countries in the 1930s. The USA had many operational radar sets at the time of Pearl Harbor. The radar on Oahu did detect the Japanese attack, but the communications with the cen...
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Chapter
Medical Imaging
Medical imaging has revolutionized modern medicine in many ways. The first form of what we refer to as medical imaging is generally credited to Wilhelm Conrad Röntgen, who went on to win the first Nobel prize ...
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Article
Variability of hair coat and skin traits as related to adaptation in Criollo Limonero cattle
The variation in hair coat and skin histology traits of Criollo Limonero cattle was analyzed using 213 Criollo Limonero females. Skin biopsies were obtained from slick-haired (N = 16) and normal-haired (N = 14) a...
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Article
A likelihood-MPEC approach to target classification
In this paper we develop a method for classifying an unknown data vector as belonging to one of several classes. This method is based on the statistical methods of maximum likehood and borrowed strength estima...
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Article
Optimal time-frequency projections for localized tomography
An algorithm for recovering a function from essentially localized values of its Radon transform and sparse nonlocal values was outlined in Reference 13. That algorithm utilized the time-frequency properties of...
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Article
Reduced motion artifacts in medical imaging by adaptive spatio-temporal reconstruction
In this paper we introduce an algorithm for imaging a time varying object \(f(\vec x,t)\) , from its projections at d...
