Signal processing metrics | Loss functions

Sum of absolute transformed differences

The sum of absolute transformed differences (SATD) is a block matching criterion widely used in fractional motion estimation for video compression. It works by taking a frequency transform, usually a Hadamard transform, of the differences between the pixels in the original block and the corresponding pixels in the block being used for comparison. The transform itself is often of a small block rather than the entire macroblock. For example, in x264, a series of 4Γ—4 blocks are transformed rather than doing the more processor-intensive 16Γ—16 transform. (Wikipedia).

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Ex: Determine the Absolute Value of a Difference Two Absolute Values |a-b|-|c-d|

This video explains how to determine the difference of two absolute values. http://mathispower4u.com

From playlist Absolute Value

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How to find the exact value by using the sum of two angles formula with tangent

πŸ‘‰ Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all

From playlist Sum and Difference Formulas

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Ex: Determine the Absolute Value of a Difference |a-b|

This video explains how to determine the absolute value of a difference of integers. http://mathispower4u.com

From playlist Absolute Value

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Solving an absolute value inequality by switching the signs

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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Solving absolute value inequalities when there are infinite many solutions

πŸ‘‰ Learn how to solve multi-step absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality where there are more terms apart from th

From playlist Solve Absolute Value Inequalities | Medium

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Learn to use summation notation for an arithmetic series to find the sum

πŸ‘‰ Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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Evaluate a given an expression as the sum or difference

πŸ‘‰ Learn how to write a given sum or difference of two angles formula expression as a single sum/difference of angles trigonometric function. To do this, we first identify the trigonometric function for which its sum/difference formula is given and identify the individual angles. Then we ca

From playlist Sum and Difference Formulas

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Lec 5 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 5: The z-transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 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.6-008 Digital Signal Processing, 1975

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Stability and Causality of LTI Systems Described by Difference Equations

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. z-transform analysis of stability and causality for systems described by linear constant-coefficient difference equations.

From playlist The z-Transform

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Lecture 5 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood finishes up on Fourier series, then he talks about the transformation Fourier series compared to the Fourier Transformations and how one gets to th

From playlist Fourier

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Evaluate an expression using the sum and difference of two angles

πŸ‘‰ Learn how to write a given sum or difference of two angles formula expression as a single sum/difference of angles trigonometric function. To do this, we first identify the trigonometric function for which its sum/difference formula is given and identify the individual angles. Then we ca

From playlist Sum and Difference Formulas

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Region of Convergence for the z-Transform

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. z-transforms of signals in general do not exist over the entire z-plane. The infinite series defining the z-transform only converges for a subset o

From playlist The z-Transform

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Solving a Two Step Absolute Value Equation

Lean how to solve absolute value equations. Absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value equations we need to create the two cases: the positive case and the neg

From playlist Solve Absolute Value Equations

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Lec 20b - Phys 237: Gravitational Waves with Kip Thorne

Watch the rest of the lectures on http://www.cosmolearning.com/courses/overview-of-gravitational-wave-science-400/ Redistributed with permission. This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and

From playlist Caltech: Gravitational Waves with Kip Thorne - CosmoLearning.com Physics

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A nice approach to a famous sum.

We present an amazing approach to calculate a well known series. Inspiration: https://math.stackexchange.com/questions/359667/sum-sum-n-0-infty-frac-1n2n13 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math

From playlist Interesting Sums

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Peter Sarnak, Summation formulae in spectral theory and number theory [2021]

A talk in honor of Zeev Rudnick's 60th birthday Peter Sarnak, Summation formulae in spectral theory and number theory (Institute for Advanced Study and Princeton University) Abstract: The Poisson Summation formula, Riemann-Guinand-Weil explicit formula, Selberg Trace Formula and Lefsche

From playlist Number Theory

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Introduction to Modular Forms - Part 1 of 8

β€œIntroduction to Modular Forms,” by Keith Conrad. Topics include Eisenstein series and q-expansions, applications to sums of squares and zeta-values, Hecke operators, eigenforms, and the L-function of a modular form. This is a video from CTNT, the Connecticut Summer School in Number Theor

From playlist CTNT 2016 - "Introduction to Modular Forms" by Keith Conrad

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Modular Forms | Modular Forms; Section 1 2

We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)

From playlist Modular Forms

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Using sigma sum notation to evaluate the partial sum

πŸ‘‰ Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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Spectra of metric graphs and crystalline measures - Peter Sarnak

Members' Seminar Topic: Spectra of metric graphs and crystalline measures Speaker: Peter Sarnak Affiliation: Professor, School of Mathematics Date: February 10, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Related pages

Hadamard transform | Sum of absolute differences