Differences

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--- hambasics:sections:wavemodulationmath [2024/11/24 12:57] – va7fi
+++ hambasics:sections:wavemodulationmath [2026/04/01 20:59] (current) – va7fi
@@ Line 1: / Line 1: @@
-~~NOTOC~~
 ====== More Details: AM / FM ======
 Here are a few more details about the AM, SSB, and FM modulation schemes introduced on the [[wavemodulation |Wave Modulation]] page.
-For both AM and FM examples, we'll Let:
+For both AM and FM examples, we'll let:
   * \$c(t) = \cos(2 \pi f_c t)\$ be the <fc #4682b4>radio carrier</fc> with frequency \$f_c\$
   * \$s(t) = \cos(2 \pi f_s t)\$ be the <fc #ff0000>baseband audio signal</fc> with frequency \$f_s\$
@@ Line 78: / Line 76: @@
 <WRAP round alert box center 80%>
-Now, it might be tempting to simply substitute this sum in the wave like so:
+It might be tempting to simply substitute this sum in the wave like so:
 \$$ \cos(2\pi f_c t) \quad \rightarrow \quad \cos\Big(\big(2\pi f_c + 2\pi k s(t)\big) t\Big) \$$
@@ Line 85: / Line 83: @@
 </WRAP>
-To solve this properly, we need some calculus and deduce the angle from our new frequency:
+To solve this properly, we need some calculus to deduce the angle from our new frequency:
 \$$ \frac{d}{dt}\theta(t) = 2\pi f_c + 2\pi k s(t) \qquad  \Rightarrow \qquad \theta(t) = 2\pi f_c t + 2\pi k \int_0^{t}s(\tau) d\tau \$$