Fast discrete orthonormal Stockwell transform. We present an efficient method for computing the discrete orthonormal Stockwell transform (DOST). The Stockwell transform (ST) is a time-frequency decomposition transform that is showing great promise in various applications, but is limited because its computation is infeasible for most applications. The DOST is a nonredundant version of the ST, solving many of the memory and computational issues. However, computing the DOST of a signal of length N using basis vectors is still 𝒪(N 2 ). The computational complexity of our method is 𝒪(NlogN), putting it in the same category as the FFT. The algorithm is based on a simple decomposition of the DOST matrix. We also explore the way to gain conjugate symmetry for the DOST and propose a variation of the parameters that exhibits symmetry, akin to the conjugate symmetry of the FFT of a real-valued signal. Our fast method works equally well on this symmetric DOST. In this paper, we provide a mathematical proof of our results and derive that the computational complexity of our algorithm is 𝒪(NlogN). Timing tests also confirm that the new method is orders-of-magnitude faster than the brute-force DOST, and they demonstrate that our fast DOST is indeed 𝒪(NlogN) in complexity.

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element