Separable Unitary Transforms:
The number of multiplications and additions required to compute transform coefficients
 in equation(4.1.3) is
 . This is too large for practical size images. If the transform is restricted to be separable, i.e
  
where
 and
 are 1-D complete orthogonal sets of basis vectors.
On imposition of completeness and orthonormality properties we can show that
   and
   are unitary matrices.i.e
Often one chooses
 same as
 , so that
 =  |
 =
Eqn (4.1.5) can be written as
 =  .
 Eqn (4.1.5) can be performed by first transforming each column of
 and then transforming each row of the result to obtain rows of
 . |
= 
= 
= 
=
= 
=
