An efficient recursive time-varying Fourier transform by using a half-sine wave window

The paper describes a new approach to the recursive time-varying Fourier transform (TVFT) or short-time Fourier transform (STFT), which corresponds to a half-sine wave moving window. The new recursive procedure is more efficient than that of the third-order real-pole window and requires about 41% of the computation required by a recursive Hamming or Hanning window. The half-sine wave window is finite, absolutely symmetric, and has negligibly small sidelobes in the frequency domain. It is shown that this half-sine wave window is better for real-time processing than a Hamming or a Hanning window due to its better utilization of signal energy. It is also indicated that the new recursive procedure operates equally well for adaptive estimation of average-based features such as lattice filter coefficients. In this case, by using the recursive half-sine wave window, only one real-multiplication operation is needed in one step of updating