Two classes of orthonormal wavelets that have simple closed form expre
ssions are derived from pulses with the raised-cosine spectrum. These
wavelets, which are bandlimited and polynomial-decaying in time, are f
ound to be particular examples of the Lemarie-Meyer wavelets. The deri
vation reveals interesting connections between wavelet construction an
d intersymbol interference (ISI)-free signaling for digital communicat
ions.