The frequencies that have been chosen to make up the scale of Western music are geometrically spaced. Thus the discrete Fourier transform (DFT), although extremely effcient in the fast Fourier transform implementation, yields components which do not map efficiently to musical frequencies. This is because the frequency components calculated with the DFT are separated by a constant frequency diff...

Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary exhibiting statistical variation that changes in space and time. Time-frequency characterization is useful for analyzing such data, seismic traces in particular. We present a novel time-frequency decomposition, which aims at depicting the nonstationary character of seismic data. The proposed ...

We discuss the shift invariant properties of a new implementation of the Discrete Wavelet Transform, which employs a dual tree of wavelet lters to obtain the real and imaginary parts of complex wavelet co-eecients. This introduces limited redundancy (2 m :1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective lters (properties l...