Systems and methods synthesize a signal from the odd harmonic frequency components of an input signal. An exemplary embodiment synthesizes a first signal with a digital to analog converter (DAC), generates a second signal from the first signal, and filters a selected one of the odd harmonic frequency components through a band pass filter to produce an output signal. The first signal is defined by a first frequency. The second signal is defined by the first frequency and includes a fundamental frequency component and plurality of odd harmonic frequency components. The output signal has a frequency substantially equal to the frequency of the selected odd harmonic frequency component.