Weighted-least-squares design of odd-order variable fractional-delay filters using coefficient-symmetry

Our previous work has shown that coefficient- symmetry can be exploited for designing high-accuracy and low-complexity even-order variable fractional-delay (VFD) finite- impulse-response (FIR) filters. This paper formulates a closed- form weighted-least-squares (WLS) design of odd-order VFD filters exploiting coefficient-symmetry. To reduce odd-order VFD filter complexity, we first derive a coefficient-symmetry for odd- order VFD filters, and then utilize the coefficient-symmetry to derive a closed-form error function of variable frequency response. Finally, minimizing the error function yields the optimal WLS design. Exploiting the coefficient-symmetry reduces the number of independent VFD filter coefficients by 50 %, and thus reduces the hardware cost and the number of multipliers by 50 %, which facilitates high-speed VFD filtering. An odd-order design example is given to illustrate that the symmetry-based WLS method can achieve comparable design accuracy with 50 % reduction of VFD filter complexity as compared with the existing odd-order WLS method without symmetry exploitation.