Control theory | Filter theory
The matched Z-transform method, also called the pole–zero mapping or pole–zero matching method, and abbreviated MPZ or MZT, is a technique for converting a continuous-time filter design to a discrete-time filter (digital filter) design. The method works by mapping all poles and zeros of the s-plane design to z-plane locations , for a sample interval . So an analog filter with transfer function: is transformed into the digital transfer function The gain must be adjusted to normalize the desired gain, typically set to match the analog filter's gain at DC by setting and and solving for . Since the mapping wraps the s-plane's axis around the z-plane's unit circle repeatedly, any zeros (or poles) greater than the Nyquist frequency will be mapped to an aliased location. In the (common) case that the analog transfer function has more poles than zeros, the zeros at may optionally be shifted down to the Nyquist frequency by putting them at , causing the transfer function to drop off as in much the same manner as with the bilinear transform (BLT). While this transform preserves stability and minimum phase, it preserves neither time- nor frequency-domain response and so is not widely used. More common methods include the BLT and impulse invariance methods. MZT does provide less high frequency response error than the BLT, however, making it easier to correct by adding additional zeros, which is called the MZTi (for "improved"). A specific application of the matched Z-transform method in the digital control field is with the Ackermann's formula, which changes the poles of the controllable system; in general from an unstable (or nearby) location to a stable location. (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
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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.
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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
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
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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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
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Inverse Systems for 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 inverse systems for linear constant-coefficient difference equations, including conditions for a stable and causal inverse s
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Nonlinear dimensionality reduction for faster kernel methods in machine learning - Christopher Musco
Computer Science/Discrete Mathematics Seminar I Topic: Nonlinear dimensionality reduction for faster kernel methods in machine learning. Speaker: Christopher Musco Affiliation: Massachusetts Institute of Technology Date: Febuary 12, 2018 For more videos, please visit http://video.ias.edu
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Lecture 14: Inspection in PatQuick, Hough Transform, Homography, Position Determination, Multi-Scale
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What Is RDD In Spark? | Apache Spark RDD Tutorial | Apache Spark Training | Edureka
** Apache Spark and Scala Certification Training: https://www.edureka.co/apache-spark-scala-certification-training ** This Edureka video on "RDD Using Spark" will provide you the detailed and comprehensive knowledge about RDD, which are considered to be the backbone of Apache Spark. You w
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7. Discrete Approximation of Continuous-Time Systems
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
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Physics 50. Math Methods. Lecture 6.1
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Excel Magic Trick 1326: Conditionally Format Text Modes: PivotTable, Array Formula or Power Query?
Download Excel Files: Start File: https://excelisfun.net/files/EMT1326Start.xlsx Finish File: https://excelisfun.net/files/EMT1325Finished.xlsx Home page: https://excelisfun.net/ See how to Conditionally Format Text Modes with: PivotTable, Array Formula or Power Query: 1. (00:17) Intr
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The Fourier Transform and Derivatives
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