  A general construction of a set of time-domain sequences with sparse periodic
correlation functions, having multiple segments of consecutive zero-values,
i.e. multiple zero correlation zones (ZCZs), is presented. All such sequences
have a common and block-repetitive structure of the positions of zeros in their
Discrete Fourier Transform (DFT) sequences, where the exact positions of zeros
in a DFT sequence do not impact the positions and sizes of ZCZs. This property
offers completely new degree of flexibility in designing signals with good
correlation properties under various spectral constraints. The non-zero values
of the DFT sequences are determined by the corresponding frequency-domain
modulation sequences, constructed as the element-by-element product of two
component sequences: a "long" one, which is common to the set of time-domain
sequences, and which controls the peak-to-average power ratio (PAPR) properties
of the time-domain sequences; and a "short" one, periodically extended to match
the length of the "long" component sequence, which controls the non-zero
crosscorrelation values of all time-domain sequences. It is shown that 0 dB
PAPR of time-domain sequences can be obtained if the "long" frequency-domain
component sequence is selected to be a modulatable constant amplitude zero
autocorrelation (MCAZAC) sequence. A generalized and simplified unified
construction of MCAZAC sequences is presented.
