The Wigner and Husimi distributions are the usual phase space representations of a quantum state. The Wigner distribution has structures of order ℏ². On the other hand, the Husimi distribution is a Gaussian smearing of the Wigner function on an area of size ℏ and then, it only displays structures of size ℏ. We have developed a phase space representation which results a Gaussian smearing of the Wigner function on an area of size ℏ^σ, with σ ≥ 1. Within this representation, the Husimi and Wigner functions are recovered when σ = 1 and σ ≳ 2 respectively. We treat the application of this intermediate representation to explore the semiclassical limit of quantum mechanics. In particular we show how this representation uncover semiclassical hyperbolic structures of chaotic eigenstates.