I am trying to understand the concept of frequency modulation. As written in Wikipedia, if I have a signal containing information $x_m(t)$ and I want to transmit it using frequency modulation, I need to determine a center frequency $f_c$ of the carrier wave, which has a constant amplitude. To do so, I define $$ f(\tau) = f_c + f_{\Delta}x_m(\tau) $$ And then, I modulate my carrier signal $$ y(t) = \cos\left(2\pi f_ct + \int\limits_0^tf_{\Delta}x_m d\tau\right) $$ Where $f_{\Delta}$ is the the peak frequency deviation, i.e the maximum shift away from $f_c$.

I understand the roll that $f_{\Delta}$ takes, but I am having troubles understanding how to calculate it. For example, I want to transmit the signal $$ x_m(t) = H(t-t_1) - H(t-(t_1+\Delta t)) + H(t-t_2) - H(t-(t_2 + \Delta t)) $$ i.e transmit a binary code in some sort. How can I find the frequency deviation? How do I calculate the carrier signal?


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