Theory and design of LDI lattice digital and switched-capacitor filters

The author presents a new method for the exact design and synthesis of lossless discrete-integrator (LDI) lattice digital and switched-capacitor (SC) filters. In the proposed design method, the entire digital and SC filter synthesis is performed directly in the discrete-time z-domain without any recourse to the concept of a continuous-time analogue prototype reference filter. Two LDI lattice digital filter structures are proposed, one of which employs a Foster-type and the other a Cauer-type (leapfrog) configuration. Both of these structures require at most n+1 digital multipliers and n+1 unit delays, where n represents the order of the transfer function to be realised. Similarly, the corresponding LDI lattice SC filters require at most n+2 operational amplifiers (single- or double-ended). A practical example is given to illustrate the design method and to compare the hardware requirement and the magnitude-frequency response sensitivity in the passband of the LDI lattice digital and SC filters with those of the corresponding bilinear LDI ladder digital and SC filters. It is shown that the proposed lattice filters exhibit superior sensitivity features despite their low hardware requirements