The increase in the throughput of digital television and radio broadcasting (DVB) channels can be achieved due to application of signals with a compact spectrum and a relatively small peak-to-average power ratio (PAPR). The reason is the usage of traveling wave tubes (TWT) for amplifying and transmitting signals from a satellite repeater in DVB-S2X systems. At the same time, given that the bandwidth allocated for transmission should be used as efficiently as possible, a high reduction rate of out-of-band emissions level is required. The most effective solution in this direction is the transition to spectrum-economic signals, such as optimal Faster-Than-Nyquist (FTN) signals, which can provide a certain reduction rate of the out-of-band emissions level and minimum acceptable PAPR. This article proposes a method for obtaining optimal FTN pulses, which have symmetry in time domain, with specified PAPR and reduction rate of out-of-band emissions for the quadrature phase shift keying (QPSK) and offset quadrature phase shift keying (OQPSK). The possibility of synthesizing signals with OQPSK modulation is presented theoretically for the first time. Optimal FTN signals can provide PAPR reduction by at most 3 dB and outperform known root raised cosine (RRC) pulses. The simulation model adopts an architecture for quadrature generation of optimal FTN signals with OQPSK modulation with blocks for adjustable pre-amplification, clipping, and power amplification. The proposed signals can be used to increase the spectral and energy efficiencies of satellite broadcasting systems, such as DVB-S2/S2X, as well as low-rate return channels of interactive broadcasting systems with a frequency resource shortage.