Difference between revisions of "ECE 280/Roberts13"

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** $$r(at)=at\,u(at)=at\,u(t)=a\,r(t)$$
 
** $$r(at)=at\,u(at)=at\,u(t)=a\,r(t)$$
 
* Unit rectangle rect($$t$$)=$$u(t+1/2)-u(t-1/2)$$
 
* Unit rectangle rect($$t$$)=$$u(t+1/2)-u(t-1/2)$$
** rect($$t/a$$) has a centered pulse of height 1 and width $$a$$
+
** rect($$t/a$$) has a centered pulse of height 1 and width $$|a|$$
 
* Unit triangle tri($$t$$)=$$r(t-1)-2r(t)+2(t+1)$$
 
* Unit triangle tri($$t$$)=$$r(t-1)-2r(t)+2(t+1)$$
** tri($$t/a$$) is a centered triangle of width $$2a$$ that peaks at a height of 1
+
** tri($$t/a$$) is a centered triangle of width $$2|a|$$ that peaks at a height of 1
 +
* Unit impulse $$\delta(t)$$ has an area of one at $$t=0$$
 +
** $$\delta(at)=\frac{1}{a}\delta(t)$$

Revision as of 22:00, 15 May 2024

Chapter 2

  • Unit step $$u(t)$$
    • $$u(at)=u(t)$$
  • Unit ramp ramp($$t$$)=$$r(t)$$=$$t\,u(t)$$
    • $$r(at)=at\,u(at)=at\,u(t)=a\,r(t)$$
  • Unit rectangle rect($$t$$)=$$u(t+1/2)-u(t-1/2)$$
    • rect($$t/a$$) has a centered pulse of height 1 and width $$|a|$$
  • Unit triangle tri($$t$$)=$$r(t-1)-2r(t)+2(t+1)$$
    • tri($$t/a$$) is a centered triangle of width $$2|a|$$ that peaks at a height of 1
  • Unit impulse $$\delta(t)$$ has an area of one at $$t=0$$
    • $$\delta(at)=\frac{1}{a}\delta(t)$$