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 1 at $$t=0$$ and is 0 otherwise
  • $$\delta(at)=\frac{1}{|a|}\delta(t)$$
• Unit periodic impulse train $$\delta_T(t)=\sum_{k=-\infty}^{\infty}\delta(t-kT)$$ (pulse train with period $$T$$)

Chapter 3

• [3.1] Unit impulse $$\delta[n]$$ has a value of 1at $$n=0$$ and is 0 otherwise
  • $$\delta[an]=\delta[n]$$
• [3.2] Unit step $$u[n]$$ is 0 for $$n<0$$ and 1 for $$n\geq 0$$
• [3.5] Unit ramp ramp[$$n$$]=$$r[n]=n\,u[n]$$
• [3.6] Unit periodic impulse train $$\delta_N[n]=\sum_{m=-\infty}^{\infty}\delta[n-mN]$$ (pulse train with period $$N$$)