Lecture 2: Initial commit

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