Zooming by Linear Interpolation

Linear interpolation is a FOH. For eg. For a 2 2 matrix

for ;

for ,

Linear interpolation along columns gives

correct expression

for ,

(corrected version )

for , )

(assume i/p image is zero outside )

Problem: Show the above result can also be obtained by convolving the 2M× 2N zero interlaced images with the array

whose origin ( m=0, n=0 ) is at the centre of the array (boxed element). Higher order interpolation is possible by padding each row and column of input image by p rows and p column of zeros and convolving it p times with H.