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18.327 Wavelets, Filter Banks and Applications (MIT) 18.327 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. 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 | Multiwavelets

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sampling terminology

Description

Overview of key sampling terminology.

Subjects

non probability sample | probability sample | non sampling error | non response | sampling error | sampling variability | sampling bias | representative sample | sampling units | sampling frame | target population | population | sample | ukoer | learning from woerk | lfwoer | uopcpdrm | work-based learning | wbl | continuous professional development | cpd | census | Social studies | L000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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Analytical Science

Description

Wales undergraduate level and as a CPD training resource

Subjects

ukoer | sfsoer | oer | open educational resources | metadata | analytical science | cpd training resource | analytical chemistry | measurement science | analytical process model | skills for analytical science | skills for analytical chemistry | analytical sample preparation | separation and concentration of analytes | units of measurement | volumetric techniques | gravimetric techniques | calibration methods | standard-addition | method of internal-standards | statistical analysis of data | measurement uncertainty | chromatographic methods | thin layer chromatography | gc | gas chromatography | hplc | high-performance liquid chromatography | capillary electrophoresis | potentiometry | ion-selective electrodes | amperometry | coulometry | plated film thickness | electromagnetic spectrum | electronic transitions | vibrational energy | comparison of spectroscopic techniques | fluorescence spectroscopy | mid infra-red spectroscopy | near infra-red spectroscopy | aas | atomic absorption spectroscopy | atomic emission spectroscopy | inductively coupled plasme emission spectroscopy | icpms | icpes | atomic fluorescence spectroscopy | comparison of elemental analysis techniques | principles of mass spectroscopy | electron impact mass spectroscopy | chemical ionisation mass spectroscopy | quadrupole mass spectroscopy | time-of-flight mass analysers | ion-trap mass analysers | off-line sampling systems | at-line sampling systems | on-line sampling systems | in-line sampling systems | performance characteristics of analytical techniques | flow injection analysis | fia | process gc | process ir | process ms | process uv/visible | quality management | quality assurance | qa | vam principles | quality control | qc | analytical method validation | analytical method performance characteristics | sampling of solids | liquids and gases | measurement of ph | karl fischer titration | uv/visible spectroscopy | beer's law | beer-lambert law | deviations from beer's law | mid ir spectroscopy | near ir spectroscopy | raman spectroscopy | fourier transform spectroscopies | x-ray methods | x-ray fluorescence spectroscopy | gc-ms | lc-ms | Physical sciences | F000

License

Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-nd/2.0/uk/ http://creativecommons.org/licenses/by-nc-nd/2.0/uk/

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18.310 Principles of Discrete Applied Mathematics (MIT) 18.310 Principles of Discrete Applied Mathematics (MIT)

Description

This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component. This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.

Subjects

probability | probability | probability theory counting | probability theory counting | pigeonhole principle | pigeonhole principle | Van der Waerden's theorem | Van der Waerden's theorem | Chernoff bounds | Chernoff bounds | counting | counting | coding | coding | sampling | sampling | random sampling | random sampling | Catalan families | Catalan families | generating functions | generating functions | chord diagrams | chord diagrams | linear programming | linear programming | simplex method | simplex method | Zero-Sum matrix | Zero-Sum matrix | network flows | network flows | maximum flow problem | maximum flow problem | sorting algorithms | sorting algorithms | QUICKSORT | QUICKSORT | median finding | median finding | sorting networks | sorting networks | Batcher's algorithm | Batcher's algorithm | Euclid's algorithm | Euclid's algorithm | Chinese Remainder Theorem | Chinese Remainder Theorem | cryptography | cryptography | RSA code | RSA code | primaility testing | primaility testing | FFT | FFT | Fast Fourier Transform | Fast Fourier Transform | Shannon's coding theorems | Shannon's coding theorems | Lempel-Ziv codes | Lempel-Ziv codes | linear codes | linear codes | hamming code | hamming code

License

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6.450 Principles of Digital Communication I (MIT) 6.450 Principles of Digital Communication I (MIT)

Description

The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | digital communication | data compression | data compression | Lempel-Ziv algorithm | Lempel-Ziv algorithm | scalar quantization | scalar quantization | vector quantization | vector quantization | sampling | sampling | aliasing | aliasing | Nyquist criterion | Nyquist criterion | PAM modulation | PAM modulation | QAM modulation | QAM modulation | signal constellations | signal constellations | finite-energy waveform spaces | finite-energy waveform spaces | detection | detection | communication system design | communication system design | wireless | wireless | discrete source encoding | discrete source encoding | memory-less sources | memory-less sources | entropy | entropy | asymptotic equipartition property | asymptotic equipartition property | Fourier series | Fourier series | Fourier transforms | Fourier transforms | sampling theorem | sampling theorem | orthonormal expansions | orthonormal expansions | random processes | random processes | linear functionals | linear functionals | theorem of irrelevance | theorem of irrelevance | Doppler spread | Doppler spread | time spread | time spread | coherence time | coherence time | coherence frequency | coherence frequency | Rayleigh fading | Rayleigh fading | Rake receivers | Rake receivers | CDMA | CDMA | code division multiple access | code division multiple access

License

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non-probability sampling

Description

Overview of probability and non-probability sampling techniques in quantitative research.

Subjects

confidence intervals | sampling error | snowball sampling | quota sampling | convenience sampling | stratification | cluster/ multi-stage random sample | stratified random sample | systematic sample | simple random sample | non-probability sample | ukoer | learning from woerk | lfwoer | uopcpdrm | work-based learning | wbl | continuous professional development | cpd | probability sample | Social studies | L000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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1.017 Computing and Data Analysis for Environmental Applications (MIT) 1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | probability | statistics | statistics | events | events | random variables | random variables | univariate distributions | univariate distributions | multivariate distributions | multivariate distributions | uncertainty propagation | uncertainty propagation | Bernoulli trials | Bernoulli trials | Poisson processed | Poisson processed | conditional probability | conditional probability | Bayes rule | Bayes rule | random sampling | random sampling | point estimation | point estimation | interval estimation | interval estimation | hypothesis testing | hypothesis testing | analysis of variance | analysis of variance | linear regression | linear regression | computational analysis | computational analysis | data analysis | data analysis | environmental engineering | environmental engineering | applications | applications | MATLAB | MATLAB | numerical modeling | numerical modeling | probabilistic concepts | probabilistic concepts | statistical methods | statistical methods | field data | field data | laboratory data | laboratory data | numerical techniques | numerical techniques | Monte Carlo simulation | Monte Carlo simulation | variability | variability | sampling | sampling | data sets | data sets | computer | computer | uncertainty | uncertainty | interpretation | interpretation | quantitative data | quantitative data

License

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.htm

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Light Trapping For Invertebrates

Description

Short video introducing and illustrating the collection of insects and other invertebrates using a light trap. Aimed at students without previous field experience of insect sampling techniques.

Subjects

terrestrial ecology | entomology | moth sampling | nocturnal insect sampling | ecology methods | ecology field techniques | invertebrate sampling | insect sampling | bioukoer | ukoer | Biological sciences | C000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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6.856J Randomized Algorithms (MIT) 6.856J Randomized Algorithms (MIT)

Description

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms. This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

Subjects

Randomized Algorithms | Randomized Algorithms | algorithms | algorithms | efficient in time and space | efficient in time and space | randomization | randomization | computational problems | computational problems | data structures | data structures | graph algorithms | graph algorithms | optimization | optimization | geometry | geometry | Markov chains | Markov chains | sampling | sampling | estimation | estimation | geometric algorithms | geometric algorithms | parallel and distributed algorithms | parallel and distributed algorithms | parallel and ditributed algorithm | parallel and ditributed algorithm | parallel and distributed algorithm | parallel and distributed algorithm | random sampling | random sampling | random selection of witnesses | random selection of witnesses | symmetry breaking | symmetry breaking | randomized computational models | randomized computational models | hash tables | hash tables | skip lists | skip lists | minimum spanning trees | minimum spanning trees | shortest paths | shortest paths | minimum cuts | minimum cuts | convex hulls | convex hulls | linear programming | linear programming | fixed dimension | fixed dimension | arbitrary dimension | arbitrary dimension | approximate counting | approximate counting | parallel algorithms | parallel algorithms | online algorithms | online algorithms | derandomization techniques | derandomization techniques | probabilistic analysis | probabilistic analysis | computational number theory | computational number theory | simplicity | simplicity | speed | speed | design | design | basic probability theory | basic probability theory | application | application | randomized complexity classes | randomized complexity classes | game-theoretic techniques | game-theoretic techniques | Chebyshev | Chebyshev | moment inequalities | moment inequalities | limited independence | limited independence | coupon collection | coupon collection | occupancy problems | occupancy problems | tail inequalities | tail inequalities | Chernoff bound | Chernoff bound | conditional expectation | conditional expectation | probabilistic method | probabilistic method | random walks | random walks | algebraic techniques | algebraic techniques | probability amplification | probability amplification | sorting | sorting | searching | searching | combinatorial optimization | combinatorial optimization | approximation | approximation | counting problems | counting problems | distributed algorithms | distributed algorithms | 6.856 | 6.856 | 18.416 | 18.416

License

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16.36 Communication Systems Engineering (MIT) 16.36 Communication Systems Engineering (MIT)

Description

This course will cover fundamentals of digital communications and networking. We will study the basics of information theory, sampling and quantization, coding, modulation, signal detection and system performance in the presence of noise. The study of data networking will include multiple access, reliable packet transmission, routing and protocols of the internet. The concepts taught in class will be discussed in the context of aerospace communication systems: aircraft communications, satellite communications, and deep space communications. This course will cover fundamentals of digital communications and networking. We will study the basics of information theory, sampling and quantization, coding, modulation, signal detection and system performance in the presence of noise. The study of data networking will include multiple access, reliable packet transmission, routing and protocols of the internet. The concepts taught in class will be discussed in the context of aerospace communication systems: aircraft communications, satellite communications, and deep space communications.

Subjects

digital communications | digital communications | networking | networking | information theory | information theory | sampling | sampling | quantization | quantization | coding | coding | modulation | modulation | signal detection | signal detection | data networking | data networking | multiple access | multiple access | packet transmission | packet transmission | routing | routing | aerospace communication | aerospace communication | aircraft communication | aircraft communication | satellite communication | satellite communication | deep space communication | deep space communication | communication systems haykin | communication systems haykin | computer networks tanenbaum | computer networks tanenbaum | communication systems engineering proakis | communication systems engineering proakis | sampling theorem | sampling theorem | entropy | entropy | signal detection in noise | signal detection in noise | delay models | delay models

License

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18.327 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 | Multiwavelets

License

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.htm

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18.327 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 | Multiwavelets

License

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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6.450 Principles of Digital Communication I (MIT)

Description

The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | data compression | Lempel-Ziv algorithm | scalar quantization | vector quantization | sampling | aliasing | Nyquist criterion | PAM modulation | QAM modulation | signal constellations | finite-energy waveform spaces | detection | communication system design | wireless | discrete source encoding | memory-less sources | entropy | asymptotic equipartition property | Fourier series | Fourier transforms | sampling theorem | orthonormal expansions | random processes | linear functionals | theorem of irrelevance | Doppler spread | time spread | coherence time | coherence frequency | Rayleigh fading | Rake receivers | CDMA | code division multiple access

License

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.htm

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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18.310 Principles of Discrete Applied Mathematics (MIT)

Description

This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.

Subjects

probability | probability theory counting | pigeonhole principle | Van der Waerden's theorem | Chernoff bounds | counting | coding | sampling | random sampling | Catalan families | generating functions | chord diagrams | linear programming | simplex method | Zero-Sum matrix | network flows | maximum flow problem | sorting algorithms | QUICKSORT | median finding | sorting networks | Batcher's algorithm | Euclid's algorithm | Chinese Remainder Theorem | cryptography | RSA code | primaility testing | FFT | Fast Fourier Transform | Shannon's coding theorems | Lempel-Ziv codes | linear codes | hamming code

License

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.htm

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Measuring flow rate of a stream

Description

A short PowerPoint presentation illustrating how flowrate of a stream can be measured Aimed at students without previous field experience of freshwater biology sampling techniques.

Subjects

freshwater ecology | biodiversity sampling | stream sampling | bioukoer | ukoer | ecology methods | ecology field techniques | Biological sciences | C000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative data

License

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.htm

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6.450 Principles of Digital Communication - I (MIT) 6.450 Principles of Digital Communication - I (MIT)

Description

6.450 was offered in Fall 2002 as a relatively new elective on digital communication. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring.Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication. 6.450 was offered in Fall 2002 as a relatively new elective on digital communication. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring.Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | digital communication | data compression | data compression | Lempel-Ziv algorithm | Lempel-Ziv algorithm | scalar quantization | scalar quantization | vector quantization | vector quantization | sampling | sampling | aliasing | aliasing | Nyquist criterion | Nyquist criterion | PAM modulation | PAM modulation | QAM modulation | QAM modulation | signal constellations | signal constellations | finite-energy waveform spaces | finite-energy waveform spaces | detection | detection | communication system design | communication system design

License

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.htm

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