ECE 280/Roberts13

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 $$t=0$$
  • $$\delta(at)=\frac{1}{|a|}\delta(t)$$