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DISCRETE-SIGNAL ANALYSIS AND DESIGN- P36

DISCRETE-SIGNAL ANALYSIS AND DESIGN- P36:Electronic circuit analysis and design projects often involve time-domain and frequency-domain characteristics that are difÞcult to work with using the traditional and laborious mathematical pencil-and-paper methods of former eras. This is especially true of certain nonlinear circuits and sys- tems that engineering students and experimenters may not yet be com- fortable with. | ADDITIONAL DISCRETE-SIGNAL ANALYSIS AND DESIGN INFORMATION 161 a 1 C - s 1 s 1 L X2 1 s X2 R Vo u s O k Q O Q O X1 s -R L -------------- -1 C b Figure A-4 Flow-chart for the network of Fig. A-2 a with no input u but with initial values of VC and IL b with no initial conditions but with a sine-wave input signal u t . The book by Dorf and Bishop explores this problem using several different methods that are very instructional but that we do not pursue in this book. The reader is encouraged to become more familiar with the network analysis methods described in this appendix. It is good practical engineering. Finally Fig. A-4 illustrates the two varieties of flow graph for the network discussed in this appendix. We can understand Fig. A-4a by referring to Eq. A-5 with u set to zero no external inputs and with initial values of VC 0 and IL 0 as shown also in Fig. A-2. In Fig. A-4b VC IL and their derivatives correspond to those in Eq. A-5 with initial conditions VC and IL set to zero as shown in Fig. A-3 and the input u drives the network from a zero start with a sine wave that starts at zero value. The output peak amplitude VO t fluctuates for at least the 1000 time increments illustrated. It is also an interesting exercise for the reader to calculate and plot the inductor voltage and current and the capacitor voltage and current as functions of time n in Figs. A-2 and A-3. 162 DISCRETE-SIGNAL ANALYSIS AND DESIGN REFERENCES Dorf R. C. and R. H. Bishop 2004 Modern Control Systems 10th ed. Prentice Hall Upper Saddle River NJ Chap. 3. Zwillinger D. Ed. 1996 CRC Standard Mathematical Tables and Formulae 30th ed. CRC Press Boca Raton FL. GLOSSARY Adjacent channel interference. One or more adjacent channel signals create interference in a desired channel by aliasing or wideband emissions. Aliasing classical . In positive-only frequency systems a signal in part of the positive-frequency region is invaded by a second signal that is in an adjacent part of the positive-frequency