On the Estimation of the Minimum Number of Distinct Multipliers in FIR Hilbert Transformers based on Frequency Transformation

Frequency Transformation (FT) is a technique to design Finite Impulse Response (FIR) filters with repeated simple identical subfilters, which allows reducing the overall number of distinct multipliers, the most costly elements in a digital filter. This paper presents a new expression to estimate the length of HTs, straightforwardly derived from the formula of I. Koichi et al. The proposed formula avoids the high error for cases with wide ripple, which is found in a previous formula used in the recently proposed approach to design FT-based FIR Hilbert Transformers (HTs) where the estimated number of distinct multipliers is minimized. It is shown that, with the proposed formula, the FT-based design of HTs can be expressed under the same optimization approach for any of the already existing FT-based architectures.