N-continuous orthogonal frequency-division multiplexing (NC-OFDM) is a promising technique to achieve significant sidelobe suppression for baseband OFDM signals. However, NC-OFDM usually has high implementation complexity that limits its practical applications. Based on conventional NC-OFDM, this paper proposes a new technique, termed time-domain N-continuous OFDM (TD-NC-OFDM), which shifts the processing burden from the frequency domain to the time domain. This is achieved by adding a smooth signal, which is linearly combined by rectangularly pulsed OFDM basis signals consisting of a novel basis set. We prove that TD-NC-OFDM with the basis set is essentially equivalent to conventional NC-OFDM. Furthermore, using the time-domain structure, an asymptotic spectrum analysis of N-continuous OFDM signals is obtained by developing a closed-form expression related to sidelobe decaying. This paper also examines the impact of TD-NC-OFDM on the received signal-to-interference-plus-noise ratio (SINR) and derives closed-form expressions.