System identification via sweep excitations suffers from transients in the case of high frequency rates and low system damping. This contribution presents a novel method for a time domain generation of sweep signals to accurately estimate the frequency response function of a linear system within a desired sweep time. The approach is based on a characteristic value for determining the harmony of a signal, which was previously presented by the authors. It has been empirically found that this characteristic value is directly related to the squared derivative of the period duration of a sweep signal. Therefore, it can be used to shape a desired frequency characteristic in a way that suppresses transient effects of the system response compared to basic sweep approaches. The method is optimized to identify a single degree of freedom oscillator via particle swarm optimization. It is shown that the identification via an envelope of the system response can be enhanced by approximately 70 % compared to basic sweep signals for a weak damped oscillator. Therefore, the approach mitigates the trade-off between time requirements and accuracy of system identification via sweep excitations, if a rough estimate of the resonant frequency and the damping ratio is available.