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

Matematika
Dasar telekomunikasi
Telekomunikasi
Pamrosésan sinyal