Improved spectral resolution via the reassigned Fourier transform
Charles R. Day, William A. Ainsworth, Georg F Meyer · The Journal of the Acoustical Society of America · 1999
A modified form of the Fourier transform, the reassigned Fourier transform (RAFT), uses phase as well as magnitude information. Its properties are shown to be superior for both pure-tone and speech signal analysis. The RAFT technique has the potential to deliver higher resolution spectrograms than the fast Fourier transform (FFT) for a given signal analysis window. The reassignment of energy with respect to both time and frequency, such that the reassignments model the time–frequency fluctuations of the sampled signal, allows the RAFT to deliver higher resolution than the FFT (with the FFT, spectral/temporal analyses place all of the energy at points lying in the center of either a time/frequency sample-window, respectively). In particular, the improved spectral resolution of the RAFT for a given signal analysis window size is compared with that of the FFT for a fundamental speech processing application: pitch tracking. The results indicate that use of the RAFT instead of the FFT allows shorter signal analysis windows to be used. The pitch tracking performance of the RAFT with short analysis windows (e.g., 25 and 12 ms) is better than the FFT. [Work supported by the UK’s EPSRC.]