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A new technique for suppressing the sideband levels in time-modulated linear arrays (TMLAs) is presented. The technique utilises the fixed bandwidth of the radiating elements of the array to act as bandpass filters to suppress the out-of-band harmonics generated by the time-modulation process. The approach is combined with a new element switching sequence that can be designed to redistribute the dominant harmonic components of the TMLA to predetermined frequencies that are outside the bandwidth of the array elements. The proposed technique does not require the use of complicated optimisation procedures to generate the TMLA switching sequences and is applicable to a TMLA configured to synthesise arbitrary low sidelobe patterns. Numerical results are presented to illustrate the proposed approach by considering a 16-element array of patch antenna elements designed to provide a -30 dB Chebyshev sidelobe level radiation pattern.