Mathematical series | Transforms | Functional analysis | Fourier analysis
Spectrum continuation analysis (SCA) is a generalization of the concept of Fourier series to non-periodic functions of which only a fragment has been sampled in the time domain. Recall that a Fourier series is only suitable to the analysis of periodic (or finite-domain) functions f(x) with period 2π. It can be expressed as an infinite series of sinusoids: where is the amplitude of the individual harmonics. In SCA however, one decomposes the spectrum into optimized discrete frequencies. As a consequence, and as the period of the sampled function is supposed to be infinite or not yet known, each of the discrete periodic functions that compose the sampled function fragment can not be considered to be a multiple of the fundamental frequency: As such, SCA does not necessarily deliver periodic functions, as would have been the case in Fourier analysis.For real-valued functions, the SCA series can be written as: where An and Bn are the series amplitudes. The amplitudes can only be solved if the series of values is previously optimized for a desired objective function (usually least residuals). is not necessarily the average value over the sampled interval: one might prefer to include predominant information on the behavior of the offset value in the time domain. (Wikipedia).
Koopman Spectral Analysis (Continuous Spectrum)
In this video, we discuss how to use Koopman theory for dynamical systems with a continuous eigenvalue spectrum. These systems are quite common, such as a pendulum, where the period deforms continuously as energy is added to the system. To handle these systems, we use a neural network a
From playlist Koopman Analysis
Parametric vs Nonparametric Spectrum Estimation
http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Introduces parametric (model-based) and nonparametric (Fourier-based) approaches to estimation of the power spectrum.
From playlist Estimation and Detection Theory
The tool that engineers use to design buildings in earthquake zones | The response spectrum
Earthquakes are one of the most destructive forces of nature. They could induce substantial movement in the ground, which results in the development of excessive forces in structural components, resulting in their failure. The intent of the analysis is to somehow predict the **maximum resp
From playlist Summer of Math Exposition Youtube Videos
Understanding Wavelets, Part 2: Types of Wavelet Transforms
Explore the workings of wavelet transforms in detail. •Try Wavelet Toolbox: https://goo.gl/m0ms9d •Ready to Buy: https://goo.gl/sMfoDr You will also learn important applications of using wavelet transforms with MATLAB®. Video Transcript: In the previous session, we discussed wavelet co
From playlist Understanding Wavelets
10b Data Analytics: Spatial Continuity
Lecture on the impact of spatial continuity to motivate characterization and modeling of spatial continuity.
From playlist Data Analytics and Geostatistics
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Representing multivariate random signals using principal components. Principal component analysis identifies the basis vectors that describe the la
From playlist Random Signal Characterization
Frequency Domain Interpretation of Sampling
http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Analysis of the effect of sampling a continuous-time signal in the frequency domain through use of the Fourier transform.
From playlist Sampling and Reconstruction of Signals
Suhasini Subba Rao: Reconciling the Gaussian and Whittle Likelihood with an application to ...
In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussia likelihood and the Whittle likelihood. We derive an exact,
From playlist Virtual Conference
The Fourier Transform and Derivatives
This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow
From playlist Fourier
Lecture 15, Discrete-Time Modulation | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 15, Discrete-Time Modulation Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
Lecture 19, Discrete-Time Sampling | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 19, Discrete-Time Sampling Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
Henryk Iwaniec, Spectral Theory of Automorphic Forms and Analytic Number Theory [2001]
Slides for this talk: https://drive.google.com/file/d/1EDyLbE9Aqk_61njU26gbYoHoR93aetAq/view?usp=sharing Henryk Iwaniec (Rutgers Univ) Spectral Theory of Automorphic Forms and Analytic Number Theory WEDNESDAY, APRIL 4, 2001 11:00 - 12:00 Conference on Automorphic Forms: Concepts, Te
From playlist Number Theory
AdS3 at the String Scale by Matthias Gaberdiel
ORGANIZERS : Pallab Basu, Avinash Dhar, Rajesh Gopakumar, R. Loganayagam, Gautam Mandal, Shiraz Minwalla, Suvrat Raju, Sandip Trivedi and Spenta Wadia DATE : 21 May 2018 to 02 June 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore In the past twenty years, the discovery of the AdS/C
From playlist AdS/CFT at 20 and Beyond
DDPS | Koopman Operator Theory for Dynamical Systems, Control and Data Analytics by Igor Mezic
Description: There is long history of use of mathematical decompositions to describe complex phenomena using simpler ingredients. One example is the decomposition of string vibrations into its primary, secondary, and higher modes. Recently, a spectral decomposition relying on Koopman opera
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Lecture 18, Discrete-Time Processing of Continuous-Time Signals | MIT RES.6.007 Signals and Systems
Lecture 18, Discrete-Time Processing of Continuous-Time Signals Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
7 Ruediger - Stochastic Integration & SDEs
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Get a Free Trial: https://goo.gl/C2Y9A5 Get Pricing Info: https://goo.gl/kDvGHt Ready to Buy: https://goo.gl/vsIeA5 Determine the period of a signal by measuring the distance between the peaks, and find peaks in a noisy signal using Signal Processing Toolbox™. For more on Signal Process
From playlist Signal Processing and Communications
Problems in the theory of automorphic forms: 45 years later Part II - Robert Langlands
Topic: Problems in the theory of automorphic forms: 45 years later Part II Speaker: Robert Langlands Date: 2014
From playlist Mathematics