Resonator-in-a-loop filter banks-based on a Lerner grouping of outputs

A frequency-sampling Fourier transform can be efficiently and robustly realized by a resonator-in-a-loop filter bank with uniformity spaced resonators. If the resonator outputs are grouped using a Lerner weighting, where alternating signs are used for each resonator output, then filter banks with greatly reduced sidelobes are obtained at the expense of wider passbands. The filters obtained by grouping the real Fourier transform outputs are linear phase and have exactly 90° phase shift differences compared to those obtained by a Lerner grouping of the imaginary outputs. This allows for the realization of very accurate Hilbert transform bandpass filters