Transforms | Laplace transforms
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation. It can be considered as a discrete-time equivalent of the Laplace transform (s-domain). This similarity is explored in the theory of time-scale calculus. Whereas the continuous-time Fourier transform is evaluated on the Laplace s-domain's imaginary line, the discrete-time Fourier transform is evaluated over the unit circle of the z-domain. What is roughly the s-domain's left half-plane, is now the inside of the complex unit circle; what is the z-domain's outside of the unit circle, roughly corresponds to the right half-plane of the s-domain. One of the means of designing digital filters is to take analog designs, subject them to a bilinear transform which maps them from the s-domain to the z-domain, and then produce the digital filter by inspection, manipulation, or numerical approximation. Such methods tend not to be accurate except in the vicinity of the complex unity, i.e. at low frequencies. (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
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
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
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
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
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
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.
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
Frequency Response Magnitude and Poles and Zeros
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Graphical interpretation of the magnitude response of a system described by a linear constant-coefficient difference equation in terms of the locati
From playlist The z-Transform
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
Lecture 22, The z-Transform | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 22, The z-Transform 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
MIT MIT 6.003 Signals and Systems, Fall 2011 View the complete course: http://ocw.mit.edu/6-003F11 Instructor: Dennis Freeman License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.003 Signals and Systems, Fall 2011
Lec 6 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 6: The inverse z-transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES.6-008 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
Lec 7 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 7: z-Transform properties 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
Lecture: The Z transform 2018-10-29
This (long) video takes you all the way through the process of understanding the Z transform and how it relates to the Laplace transform for simulation.
From playlist Discrete
Lecture 23, Mapping Continuous-Time Filters to Discrete-Time Filters | MIT RES.6.007
Lecture 23, Mapping Continuous-Time Filters to Discrete-Time Filters 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
Z Transform, a tool for solving difference equations
Difference equations, which are equations about sequences, can be solved easier with Z-Transform. Made by: Ali Hadizadeh Moghadam Background music: https://www.youtube.com/watch?v=neV3EPgvZ3g The original comic used in the intro made by: Hannah Hillam Keywords: Z-Transform, Difference Equ
From playlist Summer of Math Exposition Youtube Videos