Digital Lattice Filter Structures

The simplest form of the IIR digital filter structures is the direct-form structure, where the numerator and the denominator coefficients are directly used as multiplier coefficients in the implementation. However, this structure has very-high sensitivity. The reason for this is that the roots of a polynomial are very sensitive to the coefficients, so the poles and zeros of the given transfer function are very sensitive to the quantized multiplier coefficients [80]. With standard filters such as lowpass, highpass, and bandpass, the poles are generally crowded at angles close to the band edge. Sensitivity of the structure becomes worse as the number of crowded poles increases. This sensitivity problem can be avoided by implementing the transfer function as a sum or product of first and second-order sections, i.e., parallel or cascade form structures. However, for complex conjugate poles with small angles (e.g., narrow-band sharp-transition filters), we still have high sensitivity problems even with second order sections.