diff --git a/Courses/WB2235_Signals_and_Systems.typ b/Courses/WB2235_Signals_and_Systems.typ index 62c2934..f3ccfd5 100644 --- a/Courses/WB2235_Signals_and_Systems.typ +++ b/Courses/WB2235_Signals_and_Systems.typ @@ -1,4 +1,6 @@ #import "../template/lib.typ": * +#import "@preview/cetz:0.4.2" +#import "@preview/cetz-plot:0.1.3" #set page(paper: "a4") #show: notes.with( title: [WB2235], @@ -168,4 +170,44 @@ with: - $C$ complex number - $alpha$ complex number +in DT we change to base from $e^a$ to $alpha$. + +Differences between CT and DT: + +CT: + ++ the larger the magnitude of $omega_0$, the higher the rate of oscillation. ++ All signals with a different $omega_0$ can be distinguished from eachother. + +DT: + ++ The rate of oscillation grows when the magnitude grows to an odd multiple + of $pi$, and drops when the magnitude grows towards an even multiple of + $pi$. + ==== Unit impulse and unit step signals + +DT: + +Unit Impulse: + +$ delta [n] = cases( + 1 "if" n = 0, + 0 "if" n eq.not 0) $ + +Step: + +$ u [n] = cases( + 1 "if" n >= 0, + 0 "if" n < 0) $ + +Relation: + +$ delta [n] = u[n] - u[n-1] $ + +The DT unit impulse is the *first difference of the DT unit step*.\ +The DT unit step is the *running sum of the DT unit impulse*. + +$u[n] = sum_(k=0)^(infinity) delta [n-k]$ + += Lecture 2: Continuous and Discrete Systems