Signal processing metrics | Loss functions
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 4Γ4 blocks are transformed rather than doing the more processor-intensive 16Γ16 transform. (Wikipedia).
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
How to find the exact value by using the sum of two angles formula with tangent
π 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
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
Solving an absolute value inequality by switching the signs
π 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
Solving absolute value inequalities when there are infinite many solutions
π 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
Learn to use summation notation for an arithmetic series to find the sum
π 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
Evaluate a given an expression as the sum or difference
π 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
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
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
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
Evaluate an expression using the sum and difference of two angles
π 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
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
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
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
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
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
Introduction to Modular Forms - Part 1 of 8
βIntroduction to Modular Forms,β 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
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
Using sigma sum notation to evaluate the partial sum
π 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
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