  We studied the high-harmonic generation by the interaction of sub-cycle laser
pulses with the He atom. The sub-cycle pulses are modeled using the complex
source vector beam model, which is an exact solution to Maxwell's equations and
accurately models the sub-cycle field profiles. We observed that the harmonic
cutoff could be extended with the variation of the sub-cycle pulse duration,
mainly because of the inherent blueshift associated with shorter pulses. The
scaling laws for the harmonic yield and harmonic cutoff energy with pulse
duration and fundamental driver wavelengths are also deduced. Furthermore, a
detailed wavelet analysis of harmonic generation by sub-cycle pulses is carried
out. The appropriate filtering and superposition of the harmonics gave rise to
a single attosecond pulse of duration ~ 100 as.
