 # Online Multidimensional Convolution Calculator

This free online program calculates the Convolution matrice of two input matrices.

The Convolution Function is represented as C = A * B where A,B are inputs and the C is the convolution output.
This tool supports up to 4 dimension input matrices where each dimension can have up to 8 terms for each input.
Point to the result term to see the convolution terms used to calculate the result term.
Results will include the calculated values of the convoluded matrice as well as the equation of input terms used to calculate each term of the convoluded matrice.
Remember that altough the calculation matrices are of limited size, the actual convolution is over infinite size. This means there will be terms out of matrice bounds in the result equation which are simply 0 (inefective).

The online convolution calculator is used for math calculations, polynomial calculations, image processing or digital signal processing calculations. You may visit my Engineering page for other engineering tools. The online convolution tool helps me for error free calculations. I hope it helps to you too. Enjoy...

### A

Size: Input size Dimension sizes of input in form of (dim 4 size x dim 3 size x dim 2 size x dim 1 size)
There is no restriction on dimension sizes of being the same or being odd or even.
So 1x3x4x2 matrice with 4x2x5x8 matrice is OK.
Term index starts with 0 in each dimension.
Each number represents the number of terms of the corresponding dimension.

For example a 7th order polynomial can be entered as 1x1x1x7
An image of 3 by 3 pixels can be entered as 1x1x3x3.
A four dimension data will be NxMxKxL
Data Input data Input data in martix format or CSV format.
CSV format field is copy of the matrice format of the input data. Provided for convenience.

CSV data should be entred starting from term (0,0,0,0),(0,0,0,0),...(0,0,0,l),(1,0,0,0),...,(n,m,k,l)

Size:
Data

### Result (Matrix C)

Calculation Time: 0 ms
Print Time: 0 ms

Notes:
• Out of bound terms both in negative and positive direction are highlited red and the value of these terms are 0.
• This tool supports up to 4 dimension and 8 terms per dimension and term values can be between 0-256. If you need to calculate higher dimension and higher order convolution, contact me and I can enable the higher dimension and term calculation.
• If you just need high order polynomial (1 dimension) convolution, you may use the CRC tool. CRC tool allows up to 200 term polynomial (1 dimension) convolution.

# Convolution

Continious (analog) Discrete Convolution is always -∞ to ∞ for both dimensions and dimension sizes. It is the size of inputs that practically eliminates the terms of the convolution and makes the output convolutuon a finite sized matrice. For example a 2 dimension matrice of 2x2 can also be expressed as ...x1x1x1x2x2 where all the higher dimensions have size of 1. So when we say 3x3, we will know that it has infinite higher dimensions with size of one each and the last 2 dimension sizes are 3.
A good example to 1 dimension convolution is polynomal multiplication. A polynomial of x3+5x+1 can be represented by a ...1x4 matrice of [1,0,5,1].
A good example to 2 dimension convolution is image processing. A 3x3 pixel image can be a convolution input to b filtered.
Convolution is reflection of correlation.
The Sobel edge finding operation is a two-dimensional convolution of an input array with the special matrix.
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```Matlab convolution, convolution function, convolution fourier, image convolution, convolution theorem, discrete convolution, convolution filter are available.
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