Analytical smooth rectangular (ASR) pulses have shown to be useful in optical communications. ASR pulses can be cascaded, and therefore they can be very useful in non-return-to-zero communication protocols. Moreover, unlike super-Gaussian (SG) pulses, the propagation of ASR pulses in dispersive media can be expressed in analytical forms (in both time and frequency domains). However, the propagation of chirped ASR as well as chirped SG pulses, which are common in direct-modulation channels, cannot be expressed analytically. It is shown that by utilizing the similarity between ASR and SG pulses and applying analytical continuation, chirped ASR pulses can be rewritten in a form that does have an analytical expression in both time and spectral domains.