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hambasics:sections:wavemodulationmath [2026/04/01 20:56] – va7fihambasics:sections:wavemodulationmath [2026/04/01 20:59] (current) – va7fi
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-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) \$$ \$$ \cos(2\pi f_c t) \quad \rightarrow \quad \cos\Big(\big(2\pi f_c + 2\pi k s(t)\big) t\Big) \$$
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-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 \$$ \$$ \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 \$$
hambasics/sections/wavemodulationmath.1775102192.txt.gz · Last modified: by va7fi