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I've recently used 2.4GHz and 433MHz wireless communication modules, and I was wondering if the Arduino can only process at 16MHz(Arduino UNO's clock speed), then won't the communication modules also be limited to a maximum 16MHz?

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The frequency of a (wireless) radio is its carrier frequency. The data stream is carried on it by modulating that carrier wave in some way: by frequency-shifting, for example. A given processor could not provide data at a rate faster than its clock frequency (at least as a steady-state rate), but a packet of data, once supplied to and buffered in the radio, could then be streamed out at a speed unrelated to the physical specs of the supplier (the MCU). If the MCU had to drive the transmitter, bit-by-bit, then that would indeed limit the transmission speed.

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You need like 22kHz for "telephone quality" transfer of speech, but you can hardly articulate more than 4-5 syllables per second. The first is the carrier frequency, the other is data transfer speed. (And you usually need some time to think about what you want to say).

The wireless frequency is modulated by the transmitted signal, which must be lower than the frequency itself, to be able modulate it successfully and then be separated from it. There is also some overhead like headers stating who is transmitting, to who, how much, control sum and so. A lot of it is managed in hardware, without direct processor control. (You also do not generate the frequencies and tone in you head as values of sinus wave, you just send the modulation - talk - and the body makes its parts vibrate so fast with your breath).

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