The use of large-scale antenna systems in future commercial wireless communications is an emerging technology that uses an excess of transmit antennas to realize high spectral efficiency. Achieving potential gains with large-scale antenna arrays in practice hinges on sufficient channel estimation accuracy. Much prior work focuses on TDD based networks, relying on reciprocity between the uplink and downlink channels. However, most currently deployed commercial wireless systems are FDD based, making it difficult to exploit channel reciprocity. In massive MIMO FDD systems, the problem of channel estimation becomes even more challenging due to the attendant substantial training resources and feedback requirements which scale with the number of antennas. In this paper, we consider the problem of training sequence design that employs a set of training signals and its mapping to the training periods. We focus on reduced-dimension training sequence designs, along with transmit precoder designs, aimed at reducing both hardware complexity and power consumption. The resulting designs are extended to hybrid analog-digital beamforming systems, which employ a limited number of active RF chains for transmit precoding, by applying the Toeplitz distribution theorem to large-scale linear antenna systems. A practical guideline for training sequence parameter selection is presented along with performance analysis.