Overview

In 1994, in my role as Technical Program Chair for the 17th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, I solicited proposals for mini-symposia to provide delegates with accessible summaries of important issues in research areas outside their particular specializations. Terry Peters and his colleagues submitted a proposal for a symposium on Fourier Trans­ forms and Biomedical Engineering whose goal was ""to demystify the Fourier transform and describe its practical application in biomedi­ cal situations"". This was to be achieved by presenting the concepts in straightforward, physical terms with examples drawn for the parti­ cipants work in physiological signal analysis and medical imaging. The mini-symposia proved to be a great success and drew a large and appreciative audience. The only complaint being that the time allocated, 90 minutes, was not adequate to allow the participants to elaborate their ideas adequately. I understand that this feedback helped the authors to develop this book.

Full Product Details

Author:   Terry M. Peters ,  Jacqueline C. Williams
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1998
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.349kg
ISBN:  

9781461268499

ISBN 10:   1461268494
Pages:   199
Publication Date:   12 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1 Introduction to the Fourier Transform.- 1.1 Introduction.- 1.2 Basic Functions.- 1.3 Sines, Cosines and Composite waves.- 1.4 Orthogonality.- 1.5 Waves in time and space.- 1.6 Complex numbers. A Mathematical Tool.- 1.7 The Fourier transform.- 1.8 Fourier transforms in the physical world: The Lens as an FT computer.- 1.9 Blurring and convolution.- 1.10 The “Point” or “Impulse” response function..- 1.11 Band-limited functions.- 1.12 Summary.- 1.13 Bibliography.- 2 The 1-D Fourier Transform.- 2.1 Introduction.- 2.2 Re-visiting the Fourier transform.- 2.3 The Sampling Theorem.- 2.4 Aliasing.- 2.5 Convolution.- 2.6 Digital Filtering.- 2.7 The Power Spectrum.- 2.8 Deconvolution.- 2.9 System Identification.- 2.10 Summary.- 2.11 Bibliography.- 3 The 2-D Fourier Transform.- 3.1 Introduction.- 3.2 Linear space-invariant systems in two dimensions.- 3.3 Ideal systems.- 3.4 A simple X-ray imaging system.- 3.5 Modulation Transfer Function (MTF).- 3.6 Image processing.- 3.7 Tomography.- 3.8 Computed Tomography.- 3.9 Summary.- 3.10 Bibliography.- 4 The Fourier Transform in Magnetic Resonance Imaging.- 4.1 Introduction.- 4.2 The 2-D Fourier transform.- 4.3 Magnetic Resonance Imaging.- 4.4 MRI.- 4.5 Magnetic Resonance Spectroscopic Imaging.- 4.6 Motion in MRI.- 4.7 Conclusion.- 4.8 Bibliography.- 5 The Wavelet Transform.- 5.1 Introduction.- 5.2 Time-Frequency analysis.- 5.3 Multiresolution Analysis.- 5.4 Applications.- 5.5 Summary.- 5.6 Bibliography.- 6 The Discrete Fourier Transform and Fast Fourier Transform.- 6.1 Introduction.- 6.2 From Continuous to Discrete.- 6.3 The Discrete Fourier Transform.- 6.4 The Fast Fourier Transform.- 6.5 Caveats to using the DFT/FFT.- 6.6 Conclusion.- 6.7 Bibliography.

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