Signals and Systems

Signals and Systems

1. Signal: A fn which contains some information or the physical variation of one quantity w.r.t. other

   • Continuous Time and Discrete Time
     • CT : x (t)
     • DT: x [n]
     • CT -> Sampling -> DT
   • Conjugate Symmetric and Conjugate Skew Symmetric
     • CS: x(t) = x*(-t); x [n] = x* [-n]
     • CSS: x(t) = -x* (-t); x [n] = -x* [-n]
   • Period and Non-periodic
     • P: x (t) --> x(t+T) = x(t); for all t & T element of R-{0}; x [n] --> x[n+N] = x[n]; for all n; N element of Z-{0}
   • Energy and Power Signals
     • Energy Signal : 0 < E < infinity; P --> 0
     • Power Signal: 0 < P < infinity; E --> infinity
   • Real and Complex
     • Real : If the signal contains only real value
     • Else Complex Signal

2. System: An entity which extracts useful information from the signal or it processes the signal

   • Linear System
     • Obeys Superposition Principle
   • Time Invariant System
     • delayed version of i/p gives delayed version of o/p
   • Causal System
     • O/p depends on present and past i/p s
   • Stable System (BIBO)
     • Bounded i/p should give bounded o/p
   • Invertible System
     • x(t) must be able to be obtained from y(t)
   • Memoryless
     • O/p depend only on the present i/p