# 2D Z-transform

The 2D Z-transform, similar to the Z-transform, is used in Multidimensional signal processing to relate a two-dimensional discrete-time signal to the complex frequency domain in which the 2D surface in 4D space that the Fourier Transform lies on is known as the unit surface or unit bicircle. The 2D Z-transform is defined by where are integers and are represented by the complex numbers: The 2D Z-transform is a generalized version of the 2D Fourier transform. It converges for a much wider class of sequences, and is a helpful tool in allowing one to draw conclusions on system characteristics such as BIBO stability. It is also used to determine the connection between the input and output of a linear Shift-invariant system, such as manipulating a difference equation to determine the system's Transfer function. (Wikipedia).

Introduction to the z-Transform

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduces the definition of the z-transform, the complex plane, and the relationship between the z-transform and the discrete-time Fourier transfor

From playlist The z-Transform

Inversion of the z-Transform: Power Series Expansion

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Finding inverse z-tranforms by writing the z-transform as a power series expansion. Includes long division and inverting transcendental functions.

From playlist The z-Transform

z-Transform Analysis of LTI Systems

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduction to analysis of systems described by linear constant coefficient difference equations using the z-transform. Definition of the system fu

From playlist The z-Transform

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

Properties of the z-Transform

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Basic properties of the z-transform: linearity, convolution, differentiation of X(z), multiplication by an exponential sequence, time-shift property

From playlist The z-Transform

Inversion of the z-Transform: Partial Fraction Expansion

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Inversion of z-transforms consisting of ratios of polynomials in z^{-1} using the method of partial fraction expansion. Examples.

From playlist The z-Transform

2D Fourier Transform Explained with Examples

Explains the two dimensional (2D) Fourier Transform using examples. Related videos: (see: http://www.iaincollings.com) • Introduction to Image Processing with 2D Fourier Transform https://youtu.be/tlwIWjeuu8U • 2D Image Downsampling and Upsampling Explained with Examples https://youtu.be/L

From playlist Fourier

Poles and Zeros of z-Transforms

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Definition of poles and zeros for z-transforms that are a ratio of polynomials in z. Examples.

From playlist The z-Transform

The Two-Dimensional Discrete Fourier Transform

The two-dimensional discrete Fourier transform (DFT) is the natural extension of the one-dimensional DFT and describes two-dimensional signals like images as a weighted sum of two dimensional sinusoids. Two-dimensional sinusoids have a horizontal frequency component and a vertical frequen

From playlist Fourier

Linear Algebra for Computer Scientists. 14. 3D Transformation Matrices

Most real time animated computer games are based on 3 dimensional models composed of thousands of tiny primitive shapes such as triangles, and each vertex in a model is encoded as a vector. In this computer science video you will learn how matrices are used to transform these vectors in th

From playlist Linear Algebra for Computer Scientists

23: Time change of vectors in rotating systems

Jacob Linder: 16.02.2012, Classical mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook

Lecture 05: Spatial Transformations (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)

Lecture 07: Perspective Projection and Texture Mapping (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)

Karlheinz Gröchenig: Gabor Analysis and its Mysteries (Lecture 2)

Due to technical problems the blackboard is not visible. The lecture was held within the framework of the Hausdorff Trimester Program Mathematics of Signal Processing. In Gabor analysis one studies the construction and properties of series expansions of functions with respect to a set of

The Projective Perspective of Perspective Projection

Slim Engine (My software that I use to make this video): https://github.com/HardCoreCodin/SlimEngine 3b1b's Summer of Math Explainers competition (SoME1) landing page: https://www.3blue1brown.com/blog/some1 Music: "Memories" from Bensound.com

From playlist Summer of Math Exposition Youtube Videos

3D Graphing, 3D Camera Movement, 3D Parametric Curves & Surfaces2D | Mastering Manim Chapter 5

"The key to growth is the introduction of *higher dimensions* of consciousness into our awareness." - Lao Tzu In this video, we learn how to graph 3D Functions in Manim with Text, 3D Parametric Curves, and Parametric Surfaces TIMESTAMPS: 0:00 - Understanding Spherical Coordinates 0:51

From playlist Getting Started with Manim Cairo

Dungeon Warping via Orthographic Projections

In this video I use Orthographic Projection to simplify the structure of a 3D world rendered with a 2D aesthetic. It's also a great demonstration of the olc::PixelGameEngine Warped Decal function! Source: https://github.com/OneLoneCoder/Javidx9/blob/master/PixelGameEngine/SmallerProjects/

From playlist Interesting Programming

Impulse Response and Poles and Zeros

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. The relationship between the poles of a linear time-invariant system and the impulse response is developed using the z-transform.

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Lecture 06: 3D Rotations and Complex Representations (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)