Stockwell transform based on the quadratic-phase Hankel transform

The Stockwell transform is a reversible time-frequency analysis method that combines features of the wavelet transform and the short-time Fourier transform. However, its representation is limited to the conventional time-frequency plane, which may be inadequate for analyzing nonstationary signals with radial symmetry or quadratic phase characteristics. To address this, we proposed a new transform, named the quadratic-phase Hankel Stockwell transform (QPHST), which integrates the Stockwell framework with the quadratic-phase Hankel transform. This makes QPHST an effective tool for analyzing a wider class of nonstationary signals. Along with this development, we establish both the Parseval-type energy conservation property and a reconstruction formula for the continuous quadratic-phase Hankel Stockwell transform, with some illustrative examples. Also, we have shown that the convolution operator is also a quadratic-phase Hankel Stockwell window function.