Wiley signals and systems e book TLFe BO 429

17 13escribing Randoiii Signals 414 Example 17.6 The weak stationay random signal x ( t ) from Example 1'7.5 i s modulated by a deterministic signal r n ( f ) = sin ~ v tso , a new randnrii signal ;y(t)is created: y(tj = m(tj.r(t) sin(wt)-c(t) = ?72(tl)m(t2)piI ( t l , ti') It,, t z ) only deperids 011 thr differeiicc between the observativri times z = t~-tz (see F:xaryIiple 17.5), but, this is riot true for p, nz(tl)in(t2)= sirid1 sinwtz Therefore y ( t ) is neither st&ioriaiy nor weak stationary For cxarnple, the mean square at Liine t = & is but at lime C = 0, it is WC will now return t o the qurstion of the conditions under which wr ci>n esyrcss the rnsenible averagcs by the time average W e h s t define t,liP first-order time (17.18) cud the second-order time average (17.1'3)