# What does it mean by quantization on phase space?

Quantum mechanical particle's wavefunction are always described by position or momentum representation. Then, I found the so-called quantization on phase space. So, what does it really mean? Does it mean that we make momentum and position as basis in Hilbert space? Since position and momentum are non-commuting operator, how could we do that? Thank you

$f(q,p) \rightarrow \hat{A_f}=\int d\mu(q,p) f(q,p) | \psi \rangle \langle \psi |$