Page 191 - Intelligent Communication Systems

I 62 INTELLIGENT COMMUNICATION SYSTEMS
Using Eq, (37), Eqs. (33) and (34) become Eqs. (38) and (39), respectively.

123.4.3 Spectrum Analysis by Means of an Orthogonal Function
The Walsh function has a value of 1 or -1. It is used for spectrum analysis of dis-
crete data. The Walsh function is composed of wal(m,n), where w = 0, 1,...,N-1
and « = 0,1,..., Af- 1. The Walsh function with N= 8 is shown in Figure 12.8. In
general, the Walsh function is as follows:

where [0 ] is Gaussian and is an integer value of [m/2].
In Figure 12.8,
wal(0, ri) is a direct current
wal(l, n) wal(3, n) are the base wave
wal(2, ri) wal(4, ri) are the twofold wave
wal(7, ri) wal(0, ri) are the quadruple wave
where m is frequency, which varies between 1 and -1. m = 1 means that frequency
is once and m = 2 means that frequency is twice.
The two-dimensional Walsh function wal(/, k) is given in Eq. (43).