practical applications of fourier series

practical applications of fourier series - practical...

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practical applications of fourier series/transforms for MRI and NMR Phi Nguyen ELET 3700
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Table of Content Table of Contents. ............................................................................................................. 3 Abstract. ............................................................................................................................ 4 Introduction. ...................................................................................................................... 4 Process of MRI. ................................................................................................................. 5 Fourier Transform of MRI. ............................................................................................... 7 Spacial Frequency/Image Resolution. ............................................................................. 10 Conclusion. ..................................................................................................................... 13 Reference. ....................................................................................................................... 14 2
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Abstract: The objective is to understand how the Fourier Series/Transform is used to analyze a series of complex signals and waveforms during magnetic resonance imaging (MRI). I will be explaining the process of how the magnetic imaging is decomposed down to frequency and amplitude components in order to generate MR images. By using the Fourier transform, we then break down components in to MR signals, thus creating a k-space(which will be explained throughout my research). By adjusting the k-space, we can increase or decrease the frequency to project a desirable image, which can only be accomplished by using 2D inverse Fourier transform (which will also be discussed thoroughly). Introduction: MRI is based on the physics of Nuclear Magnetic Resonance (NMR), a property of atomic nuclei that was discovered in the 1940's and has a long history of use in chemical analyses, While Magnetic resonance imaging (MRI) have been used to generate images of the soft tissue of the human body. MRI is a diagnostic procedure that uses a combination of a large magnet, radiofrequencies, and a computer to produce detailed images of organs and structures within the body. Only recently have MRI been discovered to create images of the functioning human brain in a completely, 3
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non-invasive perspective. But in the process of using MRI and NMR, we
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practical applications of fourier series - practical...

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