The behavior of genetic motifs is determined not only by the gene-gene interactions, but also by the expression patterns of the constituent genes. Live single-molecule measurements have provided evidence that transcription initiation is a sequential process, whose kinetics plays a key role in the dynamics of mRNA and protein numbers. The extent to which it affects the behavior of cellular motifs is unknown. Here, we examine how the kinetics of transcription initiation affects the behavior of motifs performing filtering in amplitude and frequency domain. We find that the performance of each filter is degraded as transcript levels are lowered. This effect can be reduced by having a transcription process with more steps. In addition, we show that the kinetics of the stepwise transcription initiation process affects features such as filter cutoffs. These results constitute an assessment of the range of behaviors of genetic motifs as a function of the kinetics of transcription initiation, and thus will aid in tuning of synthetic motifs to attain specific characteristics without affecting their protein products.