  Digital signals are complex-valued functions on $\Z_n$. Signal sets with
certain properties are required in various communication systems. Traditional
signal sets consider only the time distortion during transmission. Recently,
signal sets against both the time and phase distortion have been studied, and
are called {\em time-phase} signal sets. Several constructions of time-phase
signal sets are available in the literature. There are a number of bounds on
time signal sets (also called codebooks). They are automatically bounds on
time-phase signal sets, but are bad bounds. The first objective of this paper
is to develop better bounds on time-phase signal sets from known bounds on time
signal sets. The second objective of this paper is to construct two series of
time-phase signal sets, one of which is optimal.
