The Self-Duality of Discrete Short-Time Fourier Transform and Its Applications

The self-duality of short-time Fourier transform (STFT) is an elegant property and is useful in shedding light on the construction of STFT and its resolution capability. In this paper, the discrete version of self-duality is studied, and the property is interpreted in the context of resolution capabilities of time frequency distributions. In addition, two applications are provided as showcases of these insights obtained from the interpretation. In the first application, the problem of STFT synthesis is considered, and self-duality serves as an important indication of whether the synthesis problem at hands is properly formulated. In the second application, a new kind of high-resolution time-frequency distribution is constructed based on the understandings obtained by contrasting two of the most popular time-frequency analysis tools, namely, the STFT and the Wigner distribution.