The homotopy deformation of a differential graded algebra (DGA), which classically gives It\^o calculus, can be applied
to noncommutative calculus. As a specific example of the deformation, we use the standard Podle\'s noncommutative sphere and its differential calculus. We then study the resulting operator on the noncommutative sphere, and its Hodge theory giving the eigenvalues and eigenforms on noncommutative sphere
