The unit step response of an LTI system
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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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The unit step response of an lti system

  • The unit step response of an LTI system


The unit step response of an lti system

  • The unit step response of an LTI system


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.


The unit step response of an lti system

  • Linear constant-coefficient difference equations

+

delay

When n 1,

Causality


The unit step response of an lti system

  • Linear constant-coefficient difference equations

+

delay

Determine A by initial condition:

When n = 0,

A = 1


The unit step response of an lti system

  • Linear constant-coefficient difference equations

+

delay

Two ways:

(1) Repeat the procedure

(2)


The unit step response of an lti system

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


The unit step response of an lti system

  • 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.


The unit step response of an lti system

  • Linear constant-coefficient difference equations

+

When t>0,

Causality

Determine A by initial condition:


The unit step response of an lti system

  • Linear constant-coefficient difference equations

+

Determine A by initial condition:

A = 1


The unit step response of an lti system

  • Linear constant-coefficient difference equations

+


The unit step response of an lti system

  • Singularity functions

Define:


The unit step response of an lti system

  • Singularity functions


The unit step response of an lti system

  • Singularity functions

k terms


The unit step response of an lti system

  • Singularity functions


The unit step response of an lti system

  • Singularity functions --- discrete time

Define:


The unit step response of an lti system

  • Singularity functions --- discrete time

Define:


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