The 802.15.4 standard says:

"In the 2450 MHz, 915 MHz, and 868 MHz bands, the half-sine pulse shape is used to represent each baseband chip and is given by:

p(t) = sin ( π t / (2 Tc) ) , 0 ≤ t ≤ 2 Tc"

According to the figures in that document, Tc is the duration of a chip, which is 0.5 microseconds for the 2.4 GHz frequency band; that is, there are 2 million chips per second.

To my understanding, that gives 2 MHz sine wave as the value of p(t). How exactly is this sine wave related to the 2.4 GHz RF signal?

That is, how does one, given the 2 MHz signal, produce the 2.4 GHz signal and vice versa? (I'm looking at various RF transceiver schematics, but my questions is more about "what is the mathematical relation?", not "which components to use?".)

The 802.15.4 standard says:

"In the 2450 MHz, 915 MHz, and 868 MHz bands, the half-sine pulse shape is used to represent each baseband chip and is given by:

$$ p(t) = sin ( π \frac{t}{2T_c}) \quad{for}\ \ 0 ≤ t ≤ 2 Tc $$

According to the figures in that document, \$T_c\$ is the duration of a chip, which is 0.5 microseconds for the 2.4 GHz frequency band; that is, there are 2 million chips per second.

To my understanding, that gives 2 MHz sine wave as the value of \$p(t)\$. How exactly is this sine wave related to the 2.4 GHz RF signal?

That is, how does one, given the 2 MHz signal, produce the 2.4 GHz signal and vice versa? (I'm looking at various RF transceiver schematics, but my questions is more about "what is the mathematical relation?", not "which components to use?".)

The 802.15.4 standard says:

"In the 2450 MHz, 915 MHz, and 868 MHz bands, the half-sine pulse shape is used to represent each baseband chip and is given by:

p(t) = sin ( π t / (2 Tc) ) , 0 ≤ t ≤ 2 Tc"

According to the figures in that document, Tc is the duration of a chip, which is 0.5 microseconds for the 2.4 GHz frequency band; that is, there are 2 million chips per second.

To my understanding, that gives 2 MHz sine wave as the value of p(t). How exactly is this sine wave related to the 2.4 GHz RF signal?

The 802.15.4 standard says:

"In the 2450 MHz, 915 MHz, and 868 MHz bands, the half-sine pulse shape is used to represent each baseband chip and is given by:

p(t) = sin ( π t / (2 Tc) ) , 0 ≤ t ≤ 2 Tc"

According to the figures in that document, Tc is the duration of a chip, which is 0.5 microseconds for the 2.4 GHz frequency band; that is, there are 2 million chips per second.

To my understanding, that gives 2 MHz sine wave as the value of p(t). How exactly is this sine wave related to the 2.4 GHz RF signal?

That is, how does one, given the 2 MHz signal, produce the 2.4 GHz signal and vice versa? (I'm looking at various RF transceiver schematics, but my questions is more about "what is the mathematical relation?", not "which components to use?".)