PPT On CT Impulse

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CT Impulse Presentation Transcript:
1.EEE223 Signals & Systems

2.Outline
CT Impulse (continued)
Systems
With and without memory
Invertible and inverse systems
Causal systems
Stable systems
Time invariant systems
Linear systems

3.CT unit impulse
Sampling property:

4.CT unit impulse
Derivatives of CT signals:

5.Systems
Transform input signals to output signals
OR
Input signals cause systems to respond in certain ways resulting in other output signals

6.Interconnections of systems
Series or cascade
Parallel
Series – parallel
Feedback interconnections

7.Properties: Memory
Without memory: Output ONLY depends on input at the same time, e.g.
                    y(t) = 2x(t) + x2(t)
With memory:

8.Properties: Memory
Simple delay: (memory)
y[n] = x[n-2]
Accumulator
What if output depends on FUTURE values?

9.Properties: Invertibility
Distinct inputs lead to distinct outputs (observe output, deduce input)
Then inverse systems possible
Encoding – decoding
Modulation – demodulation

10.Properties: Invertibility

11.Properties: Causality
 Output depends only on present and past values of input
y[n] = x[n] + x[n-1]     Causal
y(t) = x(t+1)        Non-causal
Memoryless systems are causal
What about y[n] = x[-n] ?

12.Properties: Stability
 Bounded input leads to bounded output
y[n] = 1.05 y[n-1] + x[n] ????
y[n] = nx[n] ???
tx(t)??  ex(t) ??
Find counterexamples for instability

13.Properties: Time Invariance
Time shift in input leads to identical time shift in the output
                x[n-no] ->  y[n-no]
Or
                x(t-to) -> y(t-to)

14.Properties: Time Invariance
                y[n] = nx[n]??
                y(t) = Cos(x(t))

15.Obeys principle of superposition
Additivity
    x1 + x2 -> y1 + y2
Homogeneity
    ax -> ay