Modulation circuitry is configured to generate a phase modulated signal having an output frequency that corresponds to a local oscillator (LO) signal divided by N.5. A phase locked loop (PLL) is configured to generate an LO signal having a frequency that is N.5 times the output frequency. Pulse circuitry configured to generate, based at least on a value of N, an edge signal including a pulse aligned with a positive edge of the LO signal and a pulse aligned with a negative edge of the LO signal. The edge signal is used to generate the phase modulated signal.

Modulation circuitry is configured to generate a phase modulated signal having an output frequency that corresponds to a local oscillator (LO) signal divided by N.5. A phase locked loop (PLL) is configured to generate an LO signal having a frequency that is N.5 times the output frequency. Pulse circuitry configured to generate, based at least on a value of N, an edge signal including a pulse aligned with a positive edge of the LO signal and a pulse aligned with a negative edge of the LO signal. The edge signal is used to generate the phase modulated signal.

A double frequency-shift keying modulating device includes a modulation module. The modulation module receives an oscillating signal and a digital signal, and generates a modulation output signal that has a first frequency. The first frequency is associated with a frequency of the oscillating signal and varies periodically at a second frequency. The second frequency is associated with the digital signal and the frequency of the oscillating signal.

A frequency divider apparatus includes a micro-electro-mechanical system (MEMS) divider that is configured to be driven by an input signal. The MEMS divider includes a passive mechanical device that generates multiple output signals. Each of the output signals has a frequency less than a frequency of the input signal.

A frequency divider apparatus includes a micro-electro-mechanical system (MEMS) divider that is configured to be driven by an input signal. The MEMS divider includes a passive mechanical device that generates multiple output signals. Each of the output signals has a frequency less than a frequency of the input signal.

A double frequency-shift keying modulating device includes a modulation module. The modulation module receives an oscillating signal and a digital signal, and generates a modulation output signal that has a first frequency. The first frequency is associated with a frequency of the oscillating signal and varies periodically at a second frequency. The second frequency is associated with the digital signal and the frequency of the oscillating signal.