Optimum low-order windows for discrete Fourier transform systems

Truncated series expansion is used to obtain discrete-time windows which are optimal in the least-square sense for a given number of terms. The representation suggested in the paper is so rapidly convergent that an excellent approximation to the exact least-square optimum is achieved even if only a few terms are kept. As a consequence, the resulting windows are easy to obtain and economical to implement in practical applications.