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# fs2 - x(t Cle-i3,ot r e_rs-i2att e_rs_iaot co Clei,ot...

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156 .: FOURIER SERIES However, we choose to use the mean-square error, which is mathemat icary tracti and leads us to the Fourier series; th" F;;;, series is defined in the next section To introduce the Fourier series, we consider the sum x(t) : 10 * 3cos<rr6r * 5cos(2ost * 30.) + 4 sin 3roof. This signal is easily shown to be periodic with period Ts : 2rr/,r"s.We now manr ,ii?ifffal inio a dirrerent mutt"-uii.ui iorm, i,sing E;i;;,, relation ri x(t):n*)fei,ot+ a 5 loil2rrt+20"1 2L- x(t) : (2eint21r-iz,o, + 12.5r_j",a)e_i2,ot * l.Se_joot, J + 10 + l.Jsiaot + (2.5ei"16)ei2ost a (2e_i,t2s"it,o,. Tbis eguailon c:ttt J>e e.rloresse</ttz frle compac(
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Unformatted text preview: x(t): Cle-i3,ot r e_rs-i2att * e_rs_iaot * co * Clei,ot * crsizuot *, = ), grsik,ot. k=-3 The coefficients cr, for this-series of comprex. exponential functions are ' t' o'"#;t,)"" li jl 1,rfl ;"*;r*i:i l#",,s k i n d ica te s rhe comprex con we s e e th en th at a s um.or,i n u, o-i-o ur Lii'.',T"T: ::T TJ:ffi }r,i:i :"i . complex exponentiar functions. N;;;;;;.n rhough some of the rerms a:r plex' the sum is rear. As rrrorn n"*i,-r;;;. one form of the Fourier serie. e-la\tf .y s-iQaot+s0"71 * Fourier Series Chao- o-i3a,t1- l 4 . ^ 2, [et:'ot TABLE 4.1 Coefficients for Example 4.2 ck c_k I 2 3 10 1.5 2.5 230. 2 z -90" 1.5 2.52-30" 2290"...
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