FAST: An extension of the Wavelet Synchrosqueezed Transform
Extracting frequency domain information from signals usually requires conversion from the time domain using methods such as Fourier, wavelet, or Hilbert transforms. Each method of transformation is subject to a theoretical limit on resolution due to Heisenberg’s uncertainty principle. Different methods of transformation approach this limit through different trade-offs in resolution along the frequency and time axes in the frequency domain representation. One of the better and more versatile methods of transformation is the wavelet transform, which makes a closer approach to the limit of resolution using a technique called synchrosqueezing. While this produces clearer results than the conventional wavelet transforms, it does not address a few critical areas. In complex signals that are com-posed of multiple independent components, frequency domain representation via synchrosqueezed wavelet transformation may show artifacts at the instants where components are not well separated in frequency. These artifacts significantly obscure the frequency distribution. In this paper, we present a technique that improves upon this aspect of the wavelet synchrosqueezed transform and improves resolution of the transformation. This is achieved through bypassing the limit on resolution using multiple sources of information as opposed to a single transform.