The diode modulation is an example of non-linear mixer. That is,the audio and carrier signals are mixed across the non-linear resistance of D1. The result of this mixing action is the sum and difference products,therefore the signals across D1 are the original frequencies and their sum and difference.If the carrier is 700KHz and the audio signal is 2KHz,the sum is 702KHz and the difference is 698KHz.These are the side-band frequencies.The 700KHz carriers the 2KHz audio are also present,as well as a multitude of product terms of harmonics,as produced in the non-linear mixing operation of D1. Since the resonant circuit is tuned to the carrier frequency, only the carriers sideboards pass to the output.Thus,the output of the diode modulator is a true amplitude modulated signal.