Signals and Systems

Unit -1 Introduction and Signals
Unit -2 Systems and Convolution
Unit -3 Fourier
Unit -4 Laplace Transform

Periodicity

Deduce following with possible answers as “Always/Not Always + Periodic/Aperiodic ” Answers will be different for Continues Time and Discrete Time Signals So answer separately for Continues and Discrete

                    Cases                             Continues                    Discrete

• Periodic   +  Periodic     = ________________   _______________                  (+ and -)
• Periodic   +  Aperiodic   = ________________   _______________
• Aperiodic +  Aperiodic   = ________________   _______________
• Periodic   x  Periodic     = ________________   _______________
• Periodic   x  Aperiodic   = ________________   _______________
• Aperiodic x  Aperiodic   = ________________   _______________

Energy and Power

1. All Time limited* signals are ALWAYS Energy Signals EXCEPT signals does not blow up* in between
2. All Time unlimited** signals ALWAYS have Infinite Energy  EXCEPT signal tends to zero when it approaches to infinity
3. All Periodic Signals have infinite Energy
4. All Periodic Signals are ALWAYS Power signals EXCEPT signal does not blow up in any period

*Time Limited means signal exist from t1 to t2 only (for finite time duration only)
**Time Unbounded mean At least one limit of signal touches to infinity. Signal exist either from – infinity to + infinity, t1 to +infinity or -infinity to t1

Systems (Linear, Time Invariant, Causal, Stable, Memory)

Linearity

1. “+ Constant” is always a Non- Linear System e.g. y(t) =x(t) +1
2. If output of system is not zero for zero input, system in Non Linear. y(t) =/ 0 for x(t) =0
3. Shifting (delaying or advancing) is Linear operation e.g. y(t) = x(t-1) or y(t) = x(t +1)
4. Scaling  (Compression or Expansion ) is _____?____ operation e.g.  y(t) = x(2t) or y(t) =x(t/2)

Time Invariant

1. Shifting (delaying or advancing) is _________________ e.g. y(t) = x(t-1) or y(t) = x(t +1)
2. Scaling  (Compression or Expansion ) is ____________  e.g.  y(t) = x(2t) or y(t) =x(t/2)
3. Any value of function of “time” present outside the argument of  input x( .) is ALWAYS Time Invariant system e.g. y(t) =tx(t)  or  =x(t)exp(-t)  or =x(t) + u(t)  or =x(t)+t

Causality

1. Shifting (delaying) is _________________ e.g. y(t) = x(t-1) or y(t) = x(t +1)
2. shifting (advancing) is _________________ e.g. y(t) = x(t-1) or y(t) = x(t +1)
3. Scaling (Compression)is ____________  e.g.  y(t) = x(2t) or y(t) =x(t/2)
4. Scaling (Expansion ) is ____________  e.g.  y(t) = x(2t) or y(t) =x(t/2)

Stability (BIBO)

1. .
2. .
3. .

Assignment -1 Assignment -2 Assignment -3

Exercise Sheet -1 Exercise Sheet -2