Block Function (window) rect(t/T) Can be expressed as u(T/2-t)-u(-T/2-t) – Draw u(t+T/2) first; then reverse it! Can be expressed as u(t+T/2)-u(t-T/2) Can be expressed as u(t+T/2)u(T/2-t) -T/2T/2 1 -T/2T/2 1 -T/2T/2 1 -T/2T/2
Application The rectangular pulse can be used to extract part of a signal
A Simple Cell Phone Charger Circuit (R1 is necessary) Another Application: Signal strength indicator
Mathematical Modeling Modify the unit rectangular pulse: 1.Shift to the right by To/4 2.The period is To/2 V1(t)V1(t-To)V1(t-2To)
Application of Impulse Function The unit impulse function is used to model sampling operation, i.e. the selection of a value of function at a particular time instant using analog to digital converter.
Generation of an Impulse Function Ramp function epsilon approaches 0
A system is an operation for which cause-and-effect relationship exists – Can be described by block diagrams – Denoted using transformation T[.] System behavior described by mathematical model Continuous-Time Systems T [.] X(t)y(t) (meat grinder)