Example The representation of discretetime signals in terms of impulse Convolution The representation of continuoustime signals in terms of impulse Properties of LIT systems Commutative property ID: 503931
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Slide1
The representation of discrete-time signals in terms of impulse
ExampleSlide2
The representation of discrete-time signals in terms of impulse
ConvolutionSlide3
The representation of continuous-time signals in terms of impulse
Properties of LIT systems
Commutative property
Distributive propertySlide4
Properties of LIT systems
Associative property
Causality
for t<0.
for n<0.
StabilitySlide5
The unit step response of an LTI systemSlide6
The unit step response of an LTI systemSlide7
The unit step response of an LTI systemSlide8
Linear constant-coefficient difference equations
depends on x[n].
We don’t know y[n] unless x[n] is given.
But h[n] doesn’t depend on x[n]. We should be able to obtain h[n] without x[n].
How?
Discrete Fourier transform, --- Ch. 5.
LTI system response properties, this chapter.
+
delaySlide9
Linear constant-coefficient difference equations
When n
1,
Causality
+
delaySlide10
Linear constant-coefficient difference equations
+
delay
Determine A by initial condition:
When n = 0
,
A = 1Slide11
Linear constant-coefficient difference equations
Two ways:
(1) Repeat the procedure
(2)
+
delaySlide12
The unit step response of an LTI system, continuous timeSlide13
Linear constant-coefficient difference equations
depends on x(t).
We don’t know y(t) unless x(t) is given.
But h(t) doesn’t depend on x(t). We should be able to obtain h(t) without x(t).
How?
Continuous time Fourier transform.
LTI system response properties, this chapter.
+Slide14
Linear constant-coefficient difference equations
When t>0,
Determine A by initial condition:
Causality
+Slide15
Linear constant-coefficient difference equations
Determine A by initial condition:
A = 1
+Slide16
Linear constant-coefficient difference equations
+Slide17
Singularity functions
Define: Slide18
Singularity functionsSlide19
Singularity functions
k termsSlide20
Singularity functionsSlide21
Singularity functions --- discrete time
Define: Slide22
Singularity functions --- discrete time
Define: