A non-contiguous spectral-band modulator for transmitting a waveform within two or more subbands (202, 204, 206) of a non-contiguous spectrum, the modulator comprising: a signal-trajectory memory to map an input symbol tuple to a sequence of phase values, each value of the sequence of phase values representing an instantaneous frequency of a waveform for a signal with a power spectral density that is constrained to the non-contiguous spectrum; a numerically-controlled-oscillator, NCO, component to accumulate the values of the sequence of phase values and to generate a phase-sample sequence representing phase samples of a transmit waveform; and a complex exponential element to perform an exponentiation on the phase-sample sequence and to generate a constant modulus signal sequence; a variable gain component to multiply the constant modulus signal sequence by a weighting sequence to generate an output signal sequence, the output signal sequence being constrained to a region in a complex plane while in a subband and having a controlled signal trajectory during transitions between subbands, characterised in that the signal-trajectory memory is configured to provide the sequence of phase values to the NCO component from a plurality of phase-value sequences stored in the signal-trajectory memory, wherein the input symbol tuple is mapped to the sequence of phase values from the signal-trajectory memory, wherein the signal-trajectory memory is further configured to generate the weighting sequence as selected by the input symbol tuple, and wherein application of the weighting sequence by the variable gain component is to shape an amplitude of the constant modulus signal sequence to a constrained region of the complex plane while in a subband and is configured to transition the constant modulus signal sequence to zero or near zero during transitions between subbands. a signal-trajectory memory to map an input symbol tuple to a sequence of phase values, each value of the sequence of phase values representing an instantaneous frequency of a waveform for a signal with a power spectral density that is constrained to the non-contiguous spectrum; a numerically-controlled-oscillator, NCO, component to accumulate the values of the sequence of phase values and to generate a phase-sample sequence representing phase samples of a transmit waveform; and a complex exponential element to perform an exponentiation on the phase-sample sequence and to generate a constant modulus signal sequence; a variable gain component to multiply the constant modulus signal sequence by a weighting sequence to generate an output signal sequence, the output signal sequence being constrained to a region in a complex plane while in a subband and having a controlled signal trajectory during transitions between subbands, characterised in that the signal-trajectory memory is configured to provide the sequence of phase values to the NCO component from a plurality of phase-value sequences stored in the signal-trajectory memory, wherein the input symbol tuple is mapped to the sequence of phase values from the signal-trajectory memory, wherein the signal-trajectory memory is further configured to generate the weighting sequence as selected by the input symbol tuple, and wherein application of the weighting sequence by the variable gain component is to shape an amplitude of the constant modulus signal sequence to a constrained region of the complex plane while in a subband and is configured to transition the constant modulus signal sequence to zero or near zero during transitions between subbands.