Recursive Fourier transform algorithms with integrated windowing

Recursive signal spectrum estimation algorithms based on the discrete Fourier transform (DFT) are presented in this paper. Unlike other methods of DFT evaluation, the recursive method updates the spectrum coefficients instead of calculating them from the beginning each time. Some difficulties with windowing are associated with this solution. A few developments of the classic recursive algorithm towards integration of the windowing process are proposed in this paper. They are based on a family of windows obtained by a multiple convolution of the rectangular window. Due to recursive realization the stability issues are taken in account. A solution which avoids this problem is included.