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If x is itself suitably differentiable, then from the properties of convolution, one has {} = () = {()}where denotes the derivative operator. Specifically, this holds if x is a compactly supported distribution or lies in the Sobolev space W 1,1 to ensure that the derivative is sufficiently regular for the convolution to be well-defined.
The simple MATLAB implementation below shows how color channels and grayscale channel can be extracted from an input image. I = imread ( 'I_RGB.png' ); % input color image % Output_image = color_channel(I), % where color channel could be red, green or blue.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.