A novel window for harmonic analysis

This paper presents a new window design technique and discusses its effect on the detection of harmonic signals in the presence of nearby strong harmonic interference. Four design parameters are introduced to independently control the pattern falloff rate, the overall sidelobe level, the near-sidelobe level and the depth of a steerable wide dip. Since the deep dip can be steered to any frequency the new window has effectively improved the detectability of a small tone without degrading resolvability. Contrary to the conventional approach of initially specifying the continuous weighting, the new design technique starts with constructing the spectral window which meets the specifications and then employs the fast Fourier transform to compute the discrete weighting. No iterative sampling or perturbation procedure is required. Numerous examples are given to demonstrate the flexibility of the new window. Several examples of detecting a three-tone signal have demonstrated the superiority of the new window in its detectability, resolvability, and accuracy of measuring the tone frequencies and amplitudes.