A New Rational Biquadratic Approximation of Digital Fractional Delay Filter

The fractional delay operator is also an all‐pass filter, meaning that it does not change the magnitude of any frequency component that goes through it. This paper presents novel algorithms for approximating FDO (fractional delay operator) z − m using rational biquadratic approximation. The key contribution of this approach is the development of an algorithm that is solely dependent on the delay m. The basic biquadratic transfer function, at the corner frequency, has a unity magnitude response and flat group delay characteristics. The proposed approach is based on approximating the fractional order integrodifferential operator s ± m . First, we will explain the equi‐ripple method. Then, we will convert analog to digital by applying the Backward‐Euler transformation. This will give us the corresponding digital approximation. Next, we will use the composite function rule and digital equi‐ripple approximation to approximate the ideal FDD (fractional digital delay) operator z − m . We can achieve this by using the biquadratic function as well as a biquadratic design. Finally, we show how effective this approach is by presenting several numerical examples. Unlike other approximations, this approximation is only quadratic and is ideal for real‐time applications.