Low-sensitivity digital ladder filters

A class of low-sensitivity digital ladder filters may be realized in the voltage-current domain by direct analogy with the continuous resistively terminated LC ladder filter. The problem of unrealizability that is implied by delay-free loops in the discrete signal flow graph is overcome by using transformations that correspond to LC elements that exhibit finite Cube factors. The resultant deterioration in the passband of the transfer function is determined from the Blowstein LC ladder sensitivity theory and is, thereby, shown to be low valued at high sampling frequencies. The sensitivity properties of this class of digital ladder filters are directly analogous to the LC prototype because each LC element is replaced by a digital multiplier. Consequently, if maximum power transfer is approximately maintained throughout the passband of the LC prototype, then the first-order sensitivity of the corresponding digital transfer function to multiply a coefficient quantization is necessarily low valued.