On Foundational Discretization Barriers in STFT Phase Retrieval

Abstract We prove that there exists no window function $$g \in {L^2(\mathbb {R})}$$ g ∈ L 2 ( R ) and lattice $${\mathcal {L}} \subset \mathbb {R}^2$$ ⊂ such every $$f f is determined up to a global phase by spectrogram samples $$|V_gf({\mathcal {L}})|$$ | V where $$V_gf$$ denotes the short-time Fourier transform of f with respect g . Consequently, forward operator $$\begin{aligned} \mapsto |V_gf({\mathcal {L}})| \end{aligned}$$ ↦ mapping square-integrable its on never injective quotient space "Equation missing" \sim h$$ ∼ h identifying two functions which agree multiplicative constant modulus one. will further elaborate this result point out under mild conditions {L}}$$ , produce identical but do not unimodular can be chosen real-valued. The derived results highlight in discretization STFT retrieval problem from measurements, prior restriction underlying signal proper subspace $${L^2(\mathbb inevitable.