3、正交函数集实例 例1:三角函数集{1,cos(n2t),sin(n92t),n=1,2,} 例2:虚指数函数集{ea,n=0,±1,±2,…} 是两组典型的在区间(t,t+T)(T=2r/2)上的完备正交函数集。 例3沃尔什函数 walah)是区间(0,1)的完备正交函数集 Wal(k, t)=IISgncos(k,2 m] ost Wal(0, t)=Sgn(cos Ot] =1 Wal(1, t)=Sgnlcos sgnlcos Ot]=Sgnlcos t Wal(2, t)=Sgn(cos 2 Wal(3, t)=Sgnlcos 2n](cos t]=Wal(l, t)Wal(2, t) Wal(4, t)=Sgn cos 4t] Wal(5, t)=wal(4, *wal(l, t) Wal(6, t)=Wal(4, tWal(2, t) Wal(7, t)=Wal(4, t)wal(2, twal(l, t)=Wal(6, twal(l, t)例3:沃尔什函数(walah)是区间（0，1）的完备正交函数集 例1：三角函数集{1，cos(nΩt)，sin(nΩt)，n=1,2,…} 例2:虚指数函数集{ejnΩt，n=0，±1，±2，…} 是两组典型的在区间(t0，t 0+T)(T=2π/Ω)上的完备正交函数集。 ( , ) cos( 2 ) 0 1 1 0 =    − = Wal k t Sgn k t t p r r r                  (7, ) (4, ) (2, ) (1, ) (6, ) (1, ) (6, ) (4, ) (2, ) (5, ) (4, ) (1, ) (4, ) cos 4 (3, ) cos 2 cos (1, ) (2, ) (2, ) cos 2 (1, ) cos cos0 cos (0, ) cos 0 1 Wal t Wal t Wal t Wal t Wal t Wal t Wal t Wal t Wal t Wal t Wal t Wal t Wal t Sgn t Wal t Sgn t Sgn t Wal t Wal t Wal t Sgn t Wal t Sgn t Sgn t Sgn t Wal t Sgn t = = = = = = = = = = = =       3、正交函数集实例