Beam training is one of the most important and challenging tasks in millimeter-wave and sub-terahertz communications. Novel transceiver architectures and signal processing techniques are required to avoid prohibitive training overhead when large antenna arrays with narrow beams are used. In this work, we leverage recent developments in wide range true-time-delay (TTD) analog arrays and frequency dependent probing beams to accelerate beam training. We propose an algorithm that achieves high-accuracy angle of arrival estimation with a single training symbol. Further, the impact of TTD front-end impairments on beam training accuracy is investigated, including the impact of gain, phase, and delay errors. Lastly, the study on impairments and required specifications of resolution and range of analog delay taps are used to provide a design insight of energy efficient TTD array, which employs a novel architecture with discrete-time sampling based TTD elements.