Sampled data systems and generating functions
Charles A. Halijak · NASA STI Repository (National Aeronautics and Space Administration) · 1971
The Z -transform has been known in the past a s the Bore1 transform, the generating function, the power series, and the infinite degree polynomial.Mathematicians prefer to call it "the formal power series1' because is is distinguished from power series by coefficients and radix belonging to distinct mathematical systems.Physical systems described by Z -transforms a r e fundamentally pulse amplitude modulation devices and their demodulators, Thus, the subjecl is beyond time invariant electrical network theory and requires additional preparation before relevant physical systems can be studied with ease.This report presents a lengthy and formal acquaintance with Z-transforms.A formal study of Z-transforms pays off by relegating physical applications to very easy eorolliasy status.Physical applications studied are:1.The numerical transform, the natural transition from analog to discrete systems, 2. Sampled-data feedback devices.3. Multiplexing and demultipilexing.4. Periodically reverse switched capacitor.5. Pulse code modulation decoders.6.The sampled-data servo.7. Proper and subharmonic digital filters.