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Bilinear transform

The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa.

Measurement, Overview & Discrete-time approximation

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Overview

Discrete-time approximation

Stability and minimum-phase property preserved

Transformation of a General LTI System

Example

Transformation for a general first-order continuous-time filter

General second-order biquad transformation

Frequency warping

Advanced semantic analysis

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Map overview Semantic statistics

Bilinear transform

Nodes54
Edges53
Triples37
Avg. degree1.96
Density0.037037
Components1

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Bilinear transform

Top relations

related to Transformation of a General LTI System · 14
Bilinear transform → Applying, As, Consider, Given, It, K-, K-s, LTI, Multiplying, N-1, N-2, N-P, N-Q, The
related to Frequency warping · 6
Bilinear transform → Likewise, That, The, This, To, When
related to Discrete-time approximation · 4
Bilinear transform → Laplace, Padé, The, When
related to Example · 4
Bilinear transform → As, If, RC, This
related to Stability and minimum-phase property preserved · 4
Bilinear transform → Likewise, The, Then, Thus
is a · 3
Bilinear transform → first-order Padé approximant of the natural logarithm function that is an exact mapping of the z-plane to the s-plane, one-to-one mapping, special case of a conformal mapping
related to Transformation for a general first-order continuous-time filter · 2
Bilinear transform → It, Transforming

Important terminology Word statistics

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Important terminology

displaystyle filter discrete-time continuous-time frequency transform bilinear omega transfer function response warping unit used digital s-plane system z-plane mapping circle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Bilinear transformis aspecial case of a conformal mapping0.90text
Bilinear transformis afirst-order Padé approximant of the natural logarithm function that is an exact mapping of the z-plane to the s-plane0.90text
Bilinear transformis aone-to-one mapping0.90text
Bilinear transformrelated to Discrete-time approximationThe0.60section
Bilinear transformrelated to Discrete-time approximationPadé0.60section
Bilinear transformrelated to Discrete-time approximationWhen0.60section
Bilinear transformrelated to Discrete-time approximationLaplace0.60section
Bilinear transformrelated to ExampleAs0.60section
Bilinear transformrelated to ExampleRC0.60section
Bilinear transformrelated to ExampleThis0.60section
Bilinear transformrelated to ExampleIf0.60section
Bilinear transformrelated to Frequency warpingTo0.60section

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