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By E. Askwith

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7. f-L-lU+l--'~'--'--f--1--l -1/2 x+1/2 Fig. 23. Block pulses blo(k, x) blo(m, y) for k, m = o ... , -t y Black areas represent +1, white areas O. <

7. f-L-lU+l--'~'--'--f--1--l -1/2 x+1/2 Fig. 23. Block pulses blo(k, x) blo(m, y) for k, m = o ... , -t y Black areas represent +1, white areas O. <

Evidently, powers of 2 play an important role for Walsh functions. Using Eq. -. This is the system required for a Fourier series expansion. The Fourier transform requires the system {sin2n yO, cos2n Y O} which is orthogonal in the whole interval - 00 < 0 < + CI) • Note that i is an integer and thus denumerable, while y is a real number and thus nondenumerable. The system of Walsh functions orthogonal and complete in the whole interval - 00 < 0 < + CI) is denoted by {sal(,u, 0), cal(,u, O)}, where p is a real number.

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