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Description

Fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically-derived signals, and the human source or recipient. Linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. Meets with graduate subjects MAS.510, MAS.511 but assignments differ. Fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically-derived signals, and the human source or recipient. Linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. Meets with graduate subjects MAS.510, MAS.511 but assignments differ.Subjects

Basic math concepts | Basic math concepts | Notation | Notation | Vocabulary | Vocabulary | Representation of systems | Representation of systems | Complex exponentials | Complex exponentials | Spectrum plots | Spectrum plots | AM | AM | Fourier series | Fourier series | FM | FM | Definition of orthogonality | Definition of orthogonality | Walsh functions and other basis sets | Walsh functions and other basis sets | Sampling theorem | Sampling theorem | Aliasing | Aliasing | Reconstruction | Reconstruction | Signal processing | Signal processingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications. Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.Subjects

Discrete-time filters | Discrete-time filters | convolution | convolution | Fourier transform | Fourier transform | owpass and highpass filters | owpass and highpass filters | Sampling rate change operations | Sampling rate change operations | upsampling and downsampling | upsampling and downsampling | ractional sampling | ractional sampling | interpolation | interpolation | Filter Banks | Filter Banks | time domain (Haar example) and frequency domain | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | conditions for alias cancellation and no distortion | perfect reconstruction | perfect reconstruction | halfband filters and possible factorizations | halfband filters and possible factorizations | Modulation and polyphase representations | Modulation and polyphase representations | Noble identities | Noble identities | block Toeplitz matrices and block z-transforms | block Toeplitz matrices and block z-transforms | polyphase examples | polyphase examples | Matlab wavelet toolbox | Matlab wavelet toolbox | Orthogonal filter banks | Orthogonal filter banks | paraunitary matrices | paraunitary matrices | orthogonality condition (Condition O) in the time domain | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | modulation domain and polyphase domain | Maxflat filters | Maxflat filters | Daubechies and Meyer formulas | Daubechies and Meyer formulas | Spectral factorization | Spectral factorization | Multiresolution Analysis (MRA) | Multiresolution Analysis (MRA) | requirements for MRA | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | Refinement equation | iterative and recursive solution techniques | iterative and recursive solution techniques | infinite product formula | infinite product formula | filter bank approach for computing scaling functions and wavelets | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | Orthogonal wavelet bases | connection to orthogonal filters | connection to orthogonal filters | orthogonality in the frequency domain | orthogonality in the frequency domain | Biorthogonal wavelet bases | Biorthogonal wavelet bases | Mallat pyramid algorithm | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | Accuracy of wavelet approximations (Condition A) | vanishing moments | vanishing moments | polynomial cancellation in filter banks | polynomial cancellation in filter banks | Smoothness of wavelet bases | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | convergence of the cascade algorithm (Condition E) | splines | splines | Bases vs. frames | Bases vs. frames | Signal and image processing | Signal and image processing | finite length signals | finite length signals | boundary filters and boundary wavelets | boundary filters and boundary wavelets | wavelet compression algorithms | wavelet compression algorithms | Lifting | Lifting | ladder structure for filter banks | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | lifting form of refinement equationSec | Wavelets and subdivision | Wavelets and subdivision | nonuniform grids | nonuniform grids | multiresolution for triangular meshes | multiresolution for triangular meshes | representation and compression of surfaces | representation and compression of surfaces | Numerical solution of PDEs | Numerical solution of PDEs | Galerkin approximation | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | convergence | Subdivision wavelets for integral equations | Subdivision wavelets for integral equations | Compression and convergence estimates | Compression and convergence estimates | M-band wavelets | M-band wavelets | DFT filter banks and cosine modulated filter banks | DFT filter banks and cosine modulated filter banks | Multiwavelets | MultiwaveletsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata22.058 Principles of Medical Imaging (MIT) 22.058 Principles of Medical Imaging (MIT)

Description

An introduction to the principles of tomographic imaging and its applications. It includes a series of lectures with a parallel set of recitations that provide demonstrations of basic principles. Both ionizing and non-ionizing radiation are covered, including x-ray, PET, MRI, and ultrasound. Emphasis on the physics and engineering of image formation. An introduction to the principles of tomographic imaging and its applications. It includes a series of lectures with a parallel set of recitations that provide demonstrations of basic principles. Both ionizing and non-ionizing radiation are covered, including x-ray, PET, MRI, and ultrasound. Emphasis on the physics and engineering of image formation.Subjects

general imaging principles | | general imaging principles | | linear optics | | linear optics | | ray tracing | | ray tracing | | Linear Imaging Systems | | Linear Imaging Systems | | Space Invariance | | Space Invariance | | Pin-hole camera | | Pin-hole camera | | Fourier Transformations | | Fourier Transformations | | Modulation Transfer Functions | | Modulation Transfer Functions | | Fourier convolution | | Fourier convolution | | Sampling | | Sampling | | Nyquist | | Nyquist | | counting statistics | | counting statistics | | additive noise | | additive noise | | optical imaging | | optical imaging | | Radiation types | | Radiation types | | Radiation detection | | Radiation detection | | photon detection | | photon detection | | spectra | | spectra | | attenuation | | attenuation | | Planar X-ray imaging | | Planar X-ray imaging | | Projective Imaging | | Projective Imaging | | X-ray CT | | X-ray CT | | Ultrasound | | Ultrasound | | microscopy | k-space | | microscopy | k-space | | NMR pulses | | NMR pulses | | f2-D gradient | | f2-D gradient | | spin echoes | | spin echoes | | 3-D methods of MRI | | 3-D methods of MRI | | volume localized spectroscopy | volume localized spectroscopyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This class teaches the fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically derived signals, and the human source or recipient. Topics include linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, and Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. The undergraduate subject MAS.160 meets with the two half-semester graduate subjects MAS.510 and MAS.511, but assignments differ. This class teaches the fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically derived signals, and the human source or recipient. Topics include linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, and Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. The undergraduate subject MAS.160 meets with the two half-semester graduate subjects MAS.510 and MAS.511, but assignments differ.Subjects

audio | audio | visual | visual | video | video | A/V | A/V | digital media | digital media | digital audio | digital audio | digital video | digital video | photography | photography | digitial photography | digitial photography | spectrum | spectrum | Spectrum plot | Spectrum plot | amplitude modulation | amplitude modulation | AM | AM | Fourier series | Fourier series | frequency modulation | frequency modulation | FM | FM | orthogonality | orthogonality | Walsh functions | Walsh functions | basis sets. Sampling theorem | basis sets. Sampling theorem | aliasing | aliasing | reconstruction | reconstruction | FFT | FFT | DFT | DFT | DTFT | DTFT | z-transform | z-transform | IIR | IIR | frequency response | frequency response | filter | filter | filter response | filter response | impulse response | impulse response | noise | noise | communications system | communications system | communications theory | communications theory | information theory | information theory | communication channel | communication channel | coding | coding | error correction | error correction | DSP | DSP | signal processing | signal processing | digital signal processing | digital signal processingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata22.058 Principles of Medical Imaging (MIT)

Description

An introduction to the principles of tomographic imaging and its applications. It includes a series of lectures with a parallel set of recitations that provide demonstrations of basic principles. Both ionizing and non-ionizing radiation are covered, including x-ray, PET, MRI, and ultrasound. Emphasis on the physics and engineering of image formation.Subjects

general imaging principles | | linear optics | | ray tracing | | Linear Imaging Systems | | Space Invariance | | Pin-hole camera | | Fourier Transformations | | Modulation Transfer Functions | | Fourier convolution | | Sampling | | Nyquist | | counting statistics | | additive noise | | optical imaging | | Radiation types | | Radiation detection | | photon detection | | spectra | | attenuation | | Planar X-ray imaging | | Projective Imaging | | X-ray CT | | Ultrasound | | microscopy | k-space | | NMR pulses | | f2-D gradient | | spin echoes | | 3-D methods of MRI | | volume localized spectroscopyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.Subjects

Discrete-time filters | convolution | Fourier transform | owpass and highpass filters | Sampling rate change operations | upsampling and downsampling | ractional sampling | interpolation | Filter Banks | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | perfect reconstruction | halfband filters and possible factorizations | Modulation and polyphase representations | Noble identities | block Toeplitz matrices and block z-transforms | polyphase examples | Matlab wavelet toolbox | Orthogonal filter banks | paraunitary matrices | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | Maxflat filters | Daubechies and Meyer formulas | Spectral factorization | Multiresolution Analysis (MRA) | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | iterative and recursive solution techniques | infinite product formula | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | connection to orthogonal filters | orthogonality in the frequency domain | Biorthogonal wavelet bases | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | vanishing moments | polynomial cancellation in filter banks | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | splines | Bases vs. frames | Signal and image processing | finite length signals | boundary filters and boundary wavelets | wavelet compression algorithms | Lifting | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | Wavelets and subdivision | nonuniform grids | multiresolution for triangular meshes | representation and compression of surfaces | Numerical solution of PDEs | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | Subdivision wavelets for integral equations | Compression and convergence estimates | M-band wavelets | DFT filter banks and cosine modulated filter banks | MultiwaveletsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataComputational Physics Resources - Topic 4 - Monte Carlo Integration

Description

Authors: Spencer Wheaton A collection of resources (simulations and worksheets) focusing on Monte Carlo Integration techniques. Clicked 56 times. Last clicked 07/30/2014 - 11:38. Teaching & Learning Context: These materials are suited for guided-inquiry instruction at the senior undergraduate or honours level.Subjects

Physics | Science | Downloadable Documents | Simulations | English | Post-secondary | Importance Sampling | Monte Carlo Integration | Sample MeanLicense

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See all metadataDK0435 Marketing Planning in Travel and Tourism

Description

This unit is designed to enhance a basic knowledge of marketing by providing the candidate with the opportunity to put theory into practice through the gathering of marketing information and the development of a marketing plan for a travel or tourism business, based on an assessment of the marketplace. It will also give candidates some insight into practices in marketing research and some exposure to designing and administering a questionnaire for the purposes of gathering data for travel and tourism businesses. This reflects the fact that the vast majority of businesses in Scottish tourism are small in size and are therefore unlikely to retain the services of marketing research agencies on their behalf. Although designed with a clear emphasis on the travel and tourism sector, the unit couSubjects

DK04 35 | Marketing mix | Collecting and analysing data | Presenting data | Gathering data | Sampling | marketing research process | Customer motivation | Trends in travel and tourism | Marketing audits | Organisational goals | Product development | Developing a promotional plan | B: Sales Marketing and Distribution | RETAILING | SCQF Level 8License

Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Scottish Qualification Authority (SQA), and (ii) none of these materials may be Used without the express, prior, written consent of the Colleges Open Learning Exchange Group (COLEG) and SQA, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Scottish Qualification Authority (SQA), and (ii) none of these materials may be Used without the express, prior, written consent of the Colleges Open Learning Exchange Group (COLEG) and SQA, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. Licensed to colleges in Scotland only Licensed to colleges in Scotland only http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 SQA SQASite sourced from

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See all metadataDP4635 Psychology D: The Research Process in Psychology

Description

This Unit is designed to enable you to develop your knowledge and understanding of the research process in psychology. You are required to design and implement an investigation into a psychological topic and analyse statistically the data produced. There are three Outcomes in this Unit. They are: 1. Design an investigation in psychology. 2. Conduct research into a psychological topic. 3. Analyse the data produced using inferential statistics and report on findings.Subjects

DP46 35 | Psychology | the Science | Ethics in Psychology | Planning the Research Investigation | Directional and Non-Directional | Research Design | Controlling Variables and Bias | Sampling | Data Analysis Method - Inferential | Levels of Measurement | Report Format | Attitudes to Mental Illness | Controlling Variables | Parametric and Non-Parametric | Design and Statistical Techniques | P: Health Care/Medicine/Health and Safety | SAFETY | SCQF Level 8License

Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Colleges Open Learning Exchange Group (COLEG), and (ii) none of these materials may be Used without the express, prior, written consent of COLEG, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Colleges Open Learning Exchange Group (COLEG), and (ii) none of these materials may be Used without the express, prior, written consent of COLEG, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. Licensed to colleges in Scotland only Licensed to colleges in Scotland only http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17759/LicenceCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17759/LicenceCOLEG.pdf?sequence=1 COLEG COLEGSite sourced from

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See all metadataD5NA04 Statistical Process Control

Description

Statistical process control (SPC) is a tool used to control the stability of the process equipment and process parameter(s) by collecting, charting and analysing data. This unit will develop an understanding of statistical quality techniques that are used to control processes.Subjects

D5NA 04 | Determining the capability of a process | Capability | Statistical terms | process capability study | Capability indices | Process control methods | control charts | variable data | Construct average | control limits | attributes | Sampling schemes | switching inspection | operating characteristic curve | SCQF Level 7License

Licensed to colleges in Scotland only Licensed to colleges in Scotland only Copyright Scottish Qualifications Authority - Material developed by James Watt College. This publication is licensed by SQA to COLEG for use by Scotland's colleges as commissioned materials under the terms and conditions of COLEG's Intellectual Property Rights document September 2004. No part of this publication may be reproduced without the prior written consent of COLEG and SQA. Copyright Scottish Qualifications Authority - Material developed by James Watt College. This publication is licensed by SQA to COLEG for use by Scotland's colleges as commissioned materials under the terms and conditions of COLEG's Intellectual Property Rights document September 2004. No part of this publication may be reproduced without the prior written consent of COLEG and SQA. http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 SQASite sourced from

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See all metadataDG3535 Applications of Signal Processing and Conditioning

Description

This unit is designed to enable candidates to know, understand and apply a number of signal processing techniques to the solution of filtering and control problems for implementation on a digital signal processor (DSP), microprocessor or microcontroller based system. Outcome 1 has been written to introduce the principles of sampling and reconstruction, and through practical experiment deduce the requirement for anti-aliasing and reconstruction filters. Outcome 2 then introduces a variety of approaches to digital filtering, and includes integration and differentiation, which are required later. Outcome 3 applies signal processing techniques to three-term control. On completion of this unit candidates should be able to: 1. demonstrate an understanding of the process of signal sampling and itSubjects

DG35 35 | Decibels | Bandwidth | Frequency spectrum | Sampling | reconstruction | Signal reconstruction | Aliasing | Anti-aliasing filters | Normalisation | FIR Filters | IIR filters | IIR program design | Differentiators | Integrators | SCQF Level 8License

Licensed to colleges in Scotland only Licensed to colleges in Scotland only Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Scottish Qualification Authority (SQA), and (ii) none of these materials may be Used without the express, prior, written consent of the Colleges Open Learning Exchange Group (COLEG) and SQA, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Scottish Qualification Authority (SQA), and (ii) none of these materials may be Used without the express, prior, written consent of the Colleges Open Learning Exchange Group (COLEG) and SQA, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Materials. http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 SQA SQASite sourced from

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See all metadataMAS.160 Signals, Systems, and Information for Media Technology (MIT)

Description

Fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically-derived signals, and the human source or recipient. Linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. Meets with graduate subjects MAS.510, MAS.511 but assignments differ.Subjects

Basic math concepts | Notation | Vocabulary | Representation of systems | Complex exponentials | Spectrum plots | AM | Fourier series | FM | Definition of orthogonality | Walsh functions and other basis sets | Sampling theorem | Aliasing | Reconstruction | Signal processingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.Subjects

Discrete-time filters | convolution | Fourier transform | owpass and highpass filters | Sampling rate change operations | upsampling and downsampling | ractional sampling | interpolation | Filter Banks | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | perfect reconstruction | halfband filters and possible factorizations | Modulation and polyphase representations | Noble identities | block Toeplitz matrices and block z-transforms | polyphase examples | Matlab wavelet toolbox | Orthogonal filter banks | paraunitary matrices | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | Maxflat filters | Daubechies and Meyer formulas | Spectral factorization | Multiresolution Analysis (MRA) | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | iterative and recursive solution techniques | infinite product formula | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | connection to orthogonal filters | orthogonality in the frequency domain | Biorthogonal wavelet bases | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | vanishing moments | polynomial cancellation in filter banks | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | splines | Bases vs. frames | Signal and image processing | finite length signals | boundary filters and boundary wavelets | wavelet compression algorithms | Lifting | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | Wavelets and subdivision | nonuniform grids | multiresolution for triangular meshes | representation and compression of surfaces | Numerical solution of PDEs | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | Subdivision wavelets for integral equations | Compression and convergence estimates | M-band wavelets | DFT filter banks and cosine modulated filter banks | MultiwaveletsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata22.058 Principles of Medical Imaging (MIT)

Description

An introduction to the principles of tomographic imaging and its applications. It includes a series of lectures with a parallel set of recitations that provide demonstrations of basic principles. Both ionizing and non-ionizing radiation are covered, including x-ray, PET, MRI, and ultrasound. Emphasis on the physics and engineering of image formation.Subjects

general imaging principles | | linear optics | | ray tracing | | Linear Imaging Systems | | Space Invariance | | Pin-hole camera | | Fourier Transformations | | Modulation Transfer Functions | | Fourier convolution | | Sampling | | Nyquist | | counting statistics | | additive noise | | optical imaging | | Radiation types | | Radiation detection | | photon detection | | spectra | | attenuation | | Planar X-ray imaging | | Projective Imaging | | X-ray CT | | Ultrasound | | microscopy | k-space | | NMR pulses | | f2-D gradient | | spin echoes | | 3-D methods of MRI | | volume localized spectroscopyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataMAS.160 Signals, Systems and Information for Media Technology (MIT)

Description

This class teaches the fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically derived signals, and the human source or recipient. Topics include linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, and Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. The undergraduate subject MAS.160 meets with the two half-semester graduate subjects MAS.510 and MAS.511, but assignments differ.Subjects

audio | visual | video | A/V | digital media | digital audio | digital video | photography | digitial photography | spectrum | Spectrum plot | amplitude modulation | AM | Fourier series | frequency modulation | FM | orthogonality | Walsh functions | basis sets. Sampling theorem | aliasing | reconstruction | FFT | DFT | DTFT | z-transform | IIR | frequency response | filter | filter response | impulse response | noise | communications system | communications theory | information theory | communication channel | coding | error correction | DSP | signal processing | digital signal processingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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