1) can be interpolated as periodic extension of, but now the periodicity is described by general matrixwhich can be thought of as a
set of two periodicity vectorsand
ie
2) since is periodic in both and with a period of ,
implies that is periodic in with periodicity, i.e.
because
Example: Consider the continuous band limited signal
with
,
where B is the region of finite extent called the baseband.
If we sample
with
, which corresponds to sample locations as shown in the figure.
Figure(3.2.2)
Then
will be extended with periodicity
Thus
has the following form in the plane
.
ie 
is periodic in both 
and 
with a period of 
,
implies that 
is periodic in 
with periodicity
, 
with
,
where B is the region of finite extent called the baseband. 
with
, which corresponds to sample locations as shown in the figure. 
will be extended with periodicity
Thus
has the following form in the plane
. 
