The operation of the circuit is some what straight forward.

Transistor Q1 is the switch which turns the oscillator on and off.

Resistor R1 is the bias resistor for the Base of the transistor. R1 does not provide feed-back.

Capacitor C1 is a DC blocking capacitor, os only the signal reaches the Base of the transistor [without any dc bias].

Capacitor C2 and inductor L1 form a resonant tank which constitute the oscillator.

The input gate signal is used to turn the transistor on and off.

When the transistor turns on, current is dumped into inductor L1 and the oscillator stops ringing.

When the transistor is off [not conducting] the resonant tank oscillates at the resonant frequency determined by C2 and L1.

Fr = 1 / (2 * pie * (LC)^1/2) = Resonant Frequency

Note that because there is no feedback the oscillator will only ring for a predetermined time.

So the gate period of the input signal must be less than the time before the oscillation dies out.

This transistor is either full on [saturation] or full off, it does not operate in the active region.

The oscillator does not need to be in the emitter circuit, working the same in the collector line [inverting the gate signal].

A PNP transistor could also be used in which case the oscillator will start in the opposite phase.