Why An oscillator is the circuit that converts DC power into a repeating AC waveform at a chosen frequency, usually set by a crystal or an LC tank. Every transmitter and receiver needs one: the VFO that sets your operating frequency and the local oscillator that feeds a mixer are both oscillators. In short, it is the circuit that generates a signal at a specific frequency.
Watch out The modulator choices, reactance and phase, do not create a signal on their own; they take an existing carrier and vary it to impress audio or data onto it. A low-pass filter only removes frequencies above a cutoff, it generates nothing.
Oscillator = origin of the signal. Modulators change a signal, filters remove parts of it, only the oscillator makes one.