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Signals and Systems
M. Ortigueira
July 13, 2016
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Historical recipes
Euclid’s Algorithm ( 300 BC).
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)Euler (1707 - 1783) – Function definition, transforms, series, ...
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)Euler (1707 - 1783) – Function definition, transforms, series, ...Gauss (1777 - 1855) – Least-squares; FFT
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)Euler (1707 - 1783) – Function definition, transforms, series, ...Gauss (1777 - 1855) – Least-squares; FFTFourier ( 1768 - 1830) – Fourier Series
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)Euler (1707 - 1783) – Function definition, transforms, series, ...Gauss (1777 - 1855) – Least-squares; FFTFourier ( 1768 - 1830) – Fourier SeriesCauchy ( 1789 - 1857) – Mathematical Analysis, Complex variablefunctions.
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)Euler (1707 - 1783) – Function definition, transforms, series, ...Gauss (1777 - 1855) – Least-squares; FFTFourier ( 1768 - 1830) – Fourier SeriesCauchy ( 1789 - 1857) – Mathematical Analysis, Complex variablefunctions.Heaviside ( 1850 - 1925) – Vector calculus, Differential equations,Electromanetic Theory.
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)Euler (1707 - 1783) – Function definition, transforms, series, ...Gauss (1777 - 1855) – Least-squares; FFTFourier ( 1768 - 1830) – Fourier SeriesCauchy ( 1789 - 1857) – Mathematical Analysis, Complex variablefunctions.Heaviside ( 1850 - 1925) – Vector calculus, Differential equations,Electromanetic Theory.Schuster - Periodogram (1898)
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Historical recipes
Euclid’s Algorithm ( 300 BC).Archimedes of Syracuse ( 250) – Optical processing, Integration, ...Leonardo Bonacci (1170 - 1250) – Liber Abaci (1202).Leibniz (1646 - 1716) – Differential Calculus (1675)Euler (1707 - 1783) – Function definition, transforms, series, ...Gauss (1777 - 1855) – Least-squares; FFTFourier ( 1768 - 1830) – Fourier SeriesCauchy ( 1789 - 1857) – Mathematical Analysis, Complex variablefunctions.Heaviside ( 1850 - 1925) – Vector calculus, Differential equations,Electromanetic Theory.Schuster - Periodogram (1898)Wiener (1894 1964) – Stochastic Processes, Linear and NonlinearSystems, Control, Cybernetics, ...Wiener filter; WienerKhinchin-Einstein theorem,Paley-Winer theorem,Harmonic AnalysisExtrapolation, Interpolation and Smoothing of Stationary Time SeriesM. Ortigueira (UNINOVA) Signals and Systems July 13, 2016 2 / 7
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Historical recipes
Carson (1915) – Frequency analysis of modulations. Use of LT andFT.
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Historical recipes
Carson (1915) – Frequency analysis of modulations. Use of LT andFT.
Yule (1928)-Walker (1931) – Autoregressive models
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Historical recipes
Carson (1915) – Frequency analysis of modulations. Use of LT andFT.
Yule (1928)-Walker (1931) – Autoregressive models
Kolmogorov ( 1903 - 1987) – Stochastic processes, stochasticequations, Information theory.
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Historical recipes
Carson (1915) – Frequency analysis of modulations. Use of LT andFT.
Yule (1928)-Walker (1931) – Autoregressive models
Kolmogorov ( 1903 - 1987) – Stochastic processes, stochasticequations, Information theory.
Shannon (1948) – Information Theory
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Historical recipes
Carson (1915) – Frequency analysis of modulations. Use of LT andFT.
Yule (1928)-Walker (1931) – Autoregressive models
Kolmogorov ( 1903 - 1987) – Stochastic processes, stochasticequations, Information theory.
Shannon (1948) – Information Theory
Spectral estimation – Tukey (FFT) , Bartlett, Burg.
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Historical recipes
Carson (1915) – Frequency analysis of modulations. Use of LT andFT.
Yule (1928)-Walker (1931) – Autoregressive models
Kolmogorov ( 1903 - 1987) – Stochastic processes, stochasticequations, Information theory.
Shannon (1948) – Information Theory
Spectral estimation – Tukey (FFT) , Bartlett, Burg.
Signal Analysis and Modelling – Papoullis, Jenkins, Jury, ...
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Historical recipes
Carson (1915) – Frequency analysis of modulations. Use of LT andFT.
Yule (1928)-Walker (1931) – Autoregressive models
Kolmogorov ( 1903 - 1987) – Stochastic processes, stochasticequations, Information theory.
Shannon (1948) – Information Theory
Spectral estimation – Tukey (FFT) , Bartlett, Burg.
Signal Analysis and Modelling – Papoullis, Jenkins, Jury, ...
Discrete-time Signals and Systems – Oppenheim, Kailath, Rabiner,Markel, Gray, ...
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Main “classic” themes
Transforms
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Main “classic” themes
Transforms
Filter design
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Main “classic” themes
Transforms
Filter design
Spectral estimation
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Main “classic” themes
Transforms
Filter design
Spectral estimation
Signal modelling
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Main “classic” themes
Transforms
Filter design
Spectral estimation
Signal modelling
Time-frequency analysis - Wavelets
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Main “classic” themes
Transforms
Filter design
Spectral estimation
Signal modelling
Time-frequency analysis - Wavelets
Array Signal Processing
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Main “classic” themes
Transforms
Filter design
Spectral estimation
Signal modelling
Time-frequency analysis - Wavelets
Array Signal Processing
Image Processing
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Main “classic” themes
Transforms
Filter design
Spectral estimation
Signal modelling
Time-frequency analysis - Wavelets
Array Signal Processing
Image Processing
Multirrate Systems
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Main “classic” themes
Transforms
Filter design
Spectral estimation
Signal modelling
Time-frequency analysis - Wavelets
Array Signal Processing
Image Processing
Multirrate Systems
Fuzzy systems
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More recent mathematical themes
Entropy
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More recent mathematical themes
Entropy
Fractional Systems
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More recent mathematical themes
Entropy
Fractional Systems
Time scales
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More recent mathematical themes
Entropy
Fractional Systems
Time scales
Bayesian methods
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More recent mathematical themes
Entropy
Fractional Systems
Time scales
Bayesian methods
q-derivative based systems
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More recent mathematical themes
Entropy
Fractional Systems
Time scales
Bayesian methods
q-derivative based systems
Quaternions and other geometric methods
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More recent application themes
Signal processing for heterogeneous sensor networks
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
Sampling/reconstructing of non-bandlimited signals
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
Sampling/reconstructing of non-bandlimited signals
Time variant and time-space systems
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
Sampling/reconstructing of non-bandlimited signals
Time variant and time-space systems
Signal Decompositions
ICAPCAEMDMatching pursuits
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
Sampling/reconstructing of non-bandlimited signals
Time variant and time-space systems
Signal Decompositions
ICAPCAEMDMatching pursuits
MIMO systems
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
Sampling/reconstructing of non-bandlimited signals
Time variant and time-space systems
Signal Decompositions
ICAPCAEMDMatching pursuits
MIMO systems
Large scale systems
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
Sampling/reconstructing of non-bandlimited signals
Time variant and time-space systems
Signal Decompositions
ICAPCAEMDMatching pursuits
MIMO systems
Large scale systems
Steganography, Watermarking
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More recent application themes
Signal processing for heterogeneous sensor networks
Irregular sampling
Sampling/reconstructing of non-bandlimited signals
Time variant and time-space systems
Signal Decompositions
ICAPCAEMDMatching pursuits
MIMO systems
Large scale systems
Steganography, Watermarking
. . .
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After discussion – Forecasting
Mobile phone systems
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After discussion – Forecasting
Mobile phone systems
ECG processing and other biomedical applications
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After discussion – Forecasting
Mobile phone systems
ECG processing and other biomedical applications
Tidal analysis and modeling
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After discussion – Forecasting
Mobile phone systems
ECG processing and other biomedical applications
Tidal analysis and modeling
Other geophysical applications
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After discussion – Forecasting
Mobile phone systems
ECG processing and other biomedical applications
Tidal analysis and modeling
Other geophysical applications
Multiple sensor systems
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After discussion – Forecasting
The Signals and Systems theory should be included in the basic courses inall scientific graduations.In fact it is ubiquitous.
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The End
Thanks!
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