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The unit step response of an LTI system. The unit step response of an LTI system. The unit step response of an LTI system. Linear constant-coefficient difference equations. +. delay. depends on x[n]. We don’t know y[n] unless x[n] is given.

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The unit step response of an LTI system

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#### Presentation Transcript

• The unit step response of an LTI system

• The unit step response of an LTI system

• The unit step response of an LTI system

• Linear constant-coefficient difference equations

+

delay

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?

• LTI system response properties, this chapter.

• Discrete Fourier transform, --- Ch. 5.

• Linear constant-coefficient difference equations

+

delay

When n 1,

Causality

• Linear constant-coefficient difference equations

+

delay

Determine A by initial condition:

When n = 0,

A = 1

• Linear constant-coefficient difference equations

+

delay

Two ways:

(1) Repeat the procedure

(2)

• The unit step response of an LTI system, continuous time

• 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?

• LTI system response properties, this chapter.

• Continuous time Fourier transform.

• Linear constant-coefficient difference equations

+

When t>0,

Causality

Determine A by initial condition:

• Linear constant-coefficient difference equations

+

Determine A by initial condition:

A = 1

• Linear constant-coefficient difference equations

+

• Singularity functions

Define:

• Singularity functions

• Singularity functions

k terms

• Singularity functions

• Singularity functions --- discrete time

Define:

• Singularity functions --- discrete time

Define: