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 $$ | + | ** tri($$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)$$ | ||
Latest revision as of 22:00, 15 May 2024
Chapter 2
- Unit step $$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)$$
