Chirp signals are very useful signals to cover wide frequency bands nearly instantaneously.
Chirp 101 starts with sin signals (phase aside) sweeping, liearnly or other wise, the frequency, up or down, to cover a given band [f1 f2] within certain cycle T.
HOWEVER operational chirps can and are implemented with other pulses that frequency swept sin .
The initial assumption to assume that the source may be wrong, assuming that a sawtooth is not used for chirps, that assumption is wrong.
Sawtooth pulses are rich in harmonics.
Even many conventional FM car radios use saw pulses instead of sin pulses for various purposes because saw pulses, on hardware alone, are easier to implement than clean stable pure tones.
You want to cover a wide band. f1 and f2 are not anywhere nearby, they are far apart in frequency.
Also useful : Sawtooth pulses only have one sharp step.
Assume sawtooth pulses are used as explained in the source and reword the question.