  We present a study on linear canonical transformation in the framework of a
phase space representation of quantum mechanics that we have introduced in our
previous work [1]. We begin with a brief recall about the so called phase space
representation. We give the definition of linear canonical transformation with
the transformation law of coordinate and momentum operators. We establish
successively the transformation laws of mean values, dispersions, basis state
and wave functions.Then we introduce the concept of isodispersion linear
canonical transformation.
