Coefficient-relation development and low-complexity odd-order variable-fractional-delay filter design

Variable fractional-delay (VFD) filter may have either even or odd order. This paper focuses on the development of a useful coefficient-dependence relation that exists in the odd-order VFD (OO-VFD) filter, and exploits it in designing the minimax OO-VFD filter. The design problem is first described as a quadratic cone (Qcone) programming one, and then solved by applying a Qcone programming solver. Since this coefficient-dependence relation reveals the mutual dependence between the coefficients of each subfilter pair, only nearly half of the coefficients are independent when the paired subfilters are of the same order. To further reduce the filter complexity, we adopt an optimization strategy to optimize the filter orders and make the orders unequal, which leads to a further simplified filter structure. After optimizing the unequal orders, we optimize the independent coefficients to suppress the peak error of the filter׳s frequency response. We will use an OO-VFD filter example to show that the coefficient-dependence exploitation significantly reduces the design complexity and simplifies the implementation structure.