Book contents
- Frontmatter
- Contents
- List of contributors
- Introduction
- Section 1 Image essentials
- Section 2 Biomedical images: signals to pictures
- Section 3 Image analysis
- Section 4 Biomedical applications
- Appendices
- 1 Linear systems
- 2 Fourier transform and k-space
- 3 Probability, Bayesian statistics, and information theory
- Index
1 - Linear systems
Published online by Cambridge University Press: 01 March 2011
- Frontmatter
- Contents
- List of contributors
- Introduction
- Section 1 Image essentials
- Section 2 Biomedical images: signals to pictures
- Section 3 Image analysis
- Section 4 Biomedical applications
- Appendices
- 1 Linear systems
- 2 Fourier transform and k-space
- 3 Probability, Bayesian statistics, and information theory
- Index
Summary
Objectives
Overview the concepts of systems and signals
Give examples of systems and signals in engineering, nature, and mathematics
Define the properties of linearity and shift invariance
Introduce the mathematical concepts of convolution and impulse function
Analyze input/output relationship of systems via impulse response and transfer functions
Describe discrete-time and multidimensional linear systems
Systems in engineering, biology, and mathematics
The term system has many meanings in the English language. In engineering and mathematics, we think of a system as a “black box” that accepts one or more inputs and generates some number of outputs. The external observer may not know what takes place inside the black box; but by observing the response of the system to certain test inputs, one may infer certain properties of the system. Some systems in nature behave in a very predictable manner. For example, once we have seen a magnifying glass applied to any printed image, or a megaphone applied to any person's voice, we can reliably predict how these devices would perform given any other image or voice. Other systems are more complex and less predictable. For example, if we use fMRI to measure the response of the language areas of the human cortex to hearing short sentences, the output in response to hearing “the sky is blue” is not enough to predict the response to “I love you” or to “el cielo es azul,” since the brain responds quite differently to emotionally charged stimuli and unfamiliar languages.
- Type
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- Information
- Introduction to the Science of Medical Imaging , pp. 292 - 301Publisher: Cambridge University PressPrint publication year: 2009