The square root raised cosine wavelet and its relation to the Meyer functions

A special case of the Meyer scaling function is shown to coincide with the square root raised cosine (SRRC) communication pulse, provided the fractional excess bandwidth is bounded above by one third. This pulse is widely used in digital transmission systems including the North American TDMA cellular standard. Having made this connection, we proceed to derive the time-domain SRRC wavelet in closed form. Although the SRRC wavelet with nonzero excess bandwidth reduces to the ideal sinc wavelet, allowing for a valid nonzero excess bandwidth produces a wavelet of practical interest particularly for communication applications.