Konvolusi

Dina matematika sarta, hususna, analisis fungsional, konvolusi nyaéta operator matematis anu ngajadikeun dua fungsi x1 jeung x2 jadi fungsi katilu nu dianggap salaku vérsi modifikasi tina fungsi-fungsi asal. Konvolusi mangrupa hiji alat matematika dina élmu statistik, citra, pamrosésan sinyal, sarta persamaan diférential.


 Définisi 
Konvolusi tina dua sinyal  jeung , nu dilambangkeun ku  nyaéta hiji sinyal anyar x(t) anu didéfinisikeun ku:



 Sifat konvolusi 







 Konvolusi jeung fungsi  





 Téoréma konvolusi 

Lamun  atawa  ngalambangkeun transformasi Fourier tina fungsi ,  atawa  ngalambangkeun transformasi Fourier tina fungsi , sarta  hiji konstanta, mangka:

sarta:

 Tempo ogé 

 Toeplitz matrix (convolutions can be considered a Toeplitz matrix operation where éach row is a shifted copy of the convolution kernel)
 Circulant matrix
 Cross-correlation
 Deconvolution
 Dirichlet convolution
 Titchmarsh convolution theorem
 Convolution power
 Analog signal processing
 List of convolutions of probability distributions

 Tumbu kaluar 

 http://www.nitte.ac.in/downloads/Conv-LTI.pdf 
 Convolution , on The Data Analysis BriefBook
 http://www.jhu.edu/~signals/convolve/index.html Visual convolution Java Applet.
 http://www.jhu.edu/~signals/discreteconv2/index.html Visual convolution Java Applet for Discrete Time functions.
 Lectures on Image Processing: A collection of 18 lectures in pdf format from Vanderbilt University. Lecture 7 is on 2-D convolution., by Alan Peters.
 http://www.vuse.vanderbilt.edu/~rap2/EECE253/EECE253_01_Intro.pdf 
 Convolution Kernel Mask Operation Interactive tutorial
 Convolution at MathWorld

 Rujukan 
 Hsu, Hwei P., Schaum's Outline of Théory and Problems of Analog and Digital Communications, McGraw Hill, 1993

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