Accurate estimation of the angle of departure (AoD) of the signal received from an antenna array constitutes a challenging task in applications such as initial beam acquisition or localization in the context of joint communication and sensing. In true-time-delay (TTD) arrays, by delaying the signals radiated at each antenna element proportionally to integer multiples of the reciprocal signal bandwidth, a bijective mapping between the AoD and the received signal spectrum is obtained, thus allowing for AoD estimation through spectrum analysis. Building on this concept, in this work we propose three low-complexity algorithms for AoD estimation. These algorithms are evaluated by means of proof-of-concept measurements conducted with software-defined radio (SDR) platforms. In particular, we use a uniform linear array with four antenna elements. The results show the feasibility of achieving a mean absolute errors of 3° at signal-to-noise ratios (SNRs) more than 0 dB.