2D CONVOLUTION
2016-08-23
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Aim:
To write MATLAB function for 2-D convolution.
Theory:
2-D convolution can be performed through matrix multiplication. To do this, form ,the
block matrices H0,H1 etc. from one of the matrices and block toeplitz Matrix has to be formed
from the block matrices.The other matrix is written in column form. Then the multiplication
between the block toeplitz matrix and the matrix written in column form will yield a result
similar to 2D convolution.
Let the size of the matrix x [m,n] be M1X N1 ,where M1 is the number of rows and N1 be
the number of columns of the matrix x[m,n].
. Let the size of the matrix h [m,n] be M2X N2 ,where M2 is the number of rows and N2 be
the number of columns of the matrix h[m,n].
The convolution between x(m,n) and h(m,n) is denoted by y(m,n)
Where
y(m,n)= x(m,n) * h(m,n)
The size of the matrix y [m,n] is M3X N3 ,where M3 = M1 +M2 -1 and N3 = N1+ N2 -1
To write MATLAB function for 2-D convolution.
Theory:
2-D convolution can be performed through matrix multiplication. To do this, form ,the
block matrices H0,H1 etc. from one of the matrices and block toeplitz Matrix has to be formed
from the block matrices.The other matrix is written in column form. Then the multiplication
between the block toeplitz matrix and the matrix written in column form will yield a result
similar to 2D convolution.
Let the size of the matrix x [m,n] be M1X N1 ,where M1 is the number of rows and N1 be
the number of columns of the matrix x[m,n].
. Let the size of the matrix h [m,n] be M2X N2 ,where M2 is the number of rows and N2 be
the number of columns of the matrix h[m,n].
The convolution between x(m,n) and h(m,n) is denoted by y(m,n)
Where
y(m,n)= x(m,n) * h(m,n)
The size of the matrix y [m,n] is M3X N3 ,where M3 = M1 +M2 -1 and N3 = N1+ N2 -1
matlab
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