<p>In this paper, we introduce and investigate the quadratic-phase Boas transform (QPBT), a new extension of the classical Boas transform formulated within the quadratic-phase Fourier transform domain. Building upon the quadratic-phase Hilbert transform, we construct the QPBT, establish its structural properties, and derive its transform-domain representation together with a Parseval-type identity. The interplay between the QPBT, quadratic-phase convolution, and the associated complex signal is examined in detail, and closed-form expressions for kernel-specific cases are obtained. Numerical simulations support the theoretical findings and demonstrate that the QPBT yields a stable and accurate complex-valued representation for nonstationary signals with quadratic-phase characteristics. The results confirm that this quadratic-phase generalization significantly broadens the applicability of the Boas framework in advanced time–frequency and complex-signal analysis.</p>