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Surrounding a dataset by zeros
(**zero pad**ding)
is adjoint to throwing away the extended data
(**truncation**).
Let us see why this is so.
Set a signal in a vector , and
then make a longer vector by adding some zeros at the end of .This zero padding can be regarded as the matrix multiplication
| |
(3) |

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:
| |
(4) |

So the transpose operation to zero padding data
is simply *truncating* the data back to its original length.

** Next:** Product of operators
** Up:** FAMILIAR OPERATORS
** Previous:** Transient convolution
Stanford Exploration Project

10/21/1998