The Fourier Transform in Biomedical Engineering

Terry M. Peters, Jacqueline C. Williams (Autoren)

Buch | Softcover

199 Seiten

2012 | Softcover reprint of the original 1st ed. 1998
Springer-Verlag New York Inc.
978-1-4612-6849-9 (ISBN)

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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.

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.

Reihe/Serie	Applied and Numerical Harmonic Analysis
Zusatzinfo	XIX, 199 p.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Weitere Themen ► Bioinformatik
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Medizin / Pharmazie ► Allgemeines / Lexika
	Naturwissenschaften ► Biologie
ISBN-10	1-4612-6849-4 / 1461268494
ISBN-13	978-1-4612-6849-9 / 9781461268499
Zustand	Neuware