Rational Polynomial Windows as an Alternative for Kaiser Window

摘要

Time windows applied in signal processing applications are typically used for the reduction of the spectral leakage effect caused by the finite number of discrete samples representing the analyzed signal. The spectral leakage is in fact the result of the rapid cutting of the signal which is equivalent to the application of the rectangular window. In order to reduce this phenomenon some other window functions have been proposed e.g. simple triangular window or famous raised-cosine family represented by well-known Hann, Hamming or Blackman windows [1,2]. Some other applications of the window functions are related to the reduction of the Gibbs phenomenon in the frequency domain caused by the finite order of trigonometric approximation of periodic functions as well as some applications related to short-time Fourier transform (STFT) and the design of Finite Impulse Response (FIR) filters. In many DSP applications where the number of analyzed samples is constant, there is a possibility of storing the pre-computed values of the windowing function but some adaptive signal analysis algorithms often require the usage of the windows with variable length. In such case the computational complexity of window function plays an important role, especially if the memory amount is limited.