Surrounding a dataset by zeros
(zero padding)
is adjoint to throwing away the extended data
(truncation).
Let us see why.
Set a signal in a vector , and
then to make a longer vector ,
append some zeros to .
This zero padding can be regarded as the matrix multiplication
(11)
The matrix is simply an identity matrix
above a zero matrix .
To find the transpose to zero-padding, we now transpose the matrix
and do another matrix multiply:
(12)
So the transpose operation to zero padding data
is simply truncating the data back to its original length.
Module zpad1
pads zeros on both ends of its input.
Modules for two- and three-dimensional padding are in the
library named zpad2() and zpad3().