A method is presented for the exact design and synthesis of lossless discrete-integrator (LDI) symmetrical digital and switched-capacitor (SC) filters. In the proposed method, the entire filter synthesis is performed directly in the discrete-time z-domain without any recourse to the concept of a continuous-time analog prototype reference filter. Two symmetrical digital filter structures are developed, one of which employs a Foster-type while the other employs a Cauer-type (leapfrog) configuration. The resulting digital filter structures require at most n+1 multipliers (and the same number of unit delays), where n represents the order of the corresponding transfer function. These digital filter structures are subsequently modified to obtain the corresponding SC realizations. The resulting SC structures require at most n+2 operational amplifiers (OAs), one of which acts as a pure adder (or subtractor). An example is given to illustrate the application of the proposed method to the design of an LDI symmetrical SC filter having a sixth-order elliptic bandstop magnitude-frequency characteristic.
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