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1a=a(t)q=ka(t)analogsignal),(11τ+ttRXX∞→NlimN1)()(111τ+∑=txtxiNii)(τXXR)]()([τ+txtxE)]()([txtxEτ−∞→TlimT1∫+Tdttxtx0)()(τ)(ˆτXXR)(ˆτXXRT1∫+Tdttxtx0)()(τ),(11τ+ttRfX∞→NlimN1)()(111τ+∑=txtfiNii2)(τfXR)]()([τ+txtfE)(τXfR)]()([τ+tftxE)(ˆτfXRT1∫+Tdttxtf0)()(τH(f)X(f)Y(f)=H(f)X(f)H(f)x(t)↔X(f)h(t)↔H(f)y(t)↔Y(f)=H(f)X(f)y(t)=τττdtxh∫∞∞−−)()(x(t)*h(t)y(t)x(t)h(t)f(t)π21∫∞∞−ωωωdeFtj)(F()∫∞∞−−dtetftjω)(F())(ωXXS)(ωfXS)(ωXXS∫∞∞−−ττωτdeRjXX)()(ωfXS∫∞∞−−ττωτdeRjfX)(z=x+jyxyx=Re[z],y=Im[z]j=1−1z±2z)(21xx±j)(21yy±1z2z)(11jyx+)(22jyx+)(2121yyxx−)(2112yxyx+2zz=1z2z≠21zz22222121yxyyxx++22222112yxyxyx+−3*z*z=x-jy(1z±2z)**1z±*2z(1z2z)**1z*2z(1z2z)**1z*2z(*z)*=z,z*z22yx+2||zz*z2Re[z]z-*z2jIm[z]zzz=rθjerzz22yx+arctg(y/x)1z11θjer2z22θjer1z2z)(2121θθ+jerr1z2z(1r/2r))(21θθ−jenznrθjne)/1(nz)/1(nrnje/θw=f(z)zzz=f(z)zw'w=f(z)'z=()w=f(z)f(z)0z0zf(z)0zf(z)f(z)f(z)0z0zf(z)expz=ze=jyxe+2kjlnz=ln|z|+jnz)/1(nzcosz=)(jzjzee−+/2,sinz=)(jzjzee−−/2jchz=)(zzee−+/2,shz=)(zzee−−/2∫Cdzzf)(∞→nlim∑=∆nkkkzf1)(ξCf(z)C∫Cdzzf)(f(z)C0zC)(0zfjπ21dzzzzfC∫−0)({nα}{nnjba+}n=1,2,3,4∑∞=1nnα1α2αnα∑∞=0nnnzC0CzC122zCnnzCf(z)=∑∞=−00)(nnnzzCnC!1n)(0)(zfnn=0,1,2,f(z)1R0zz−2Rf(z)=∑∞−∞=−nnnzzC)(0nCjπ21ξξξdzfCn∫+−10)()(n=0,1,2,C0znCf(z)0z0z0zz−δ0zf(z)00zz−δf(z)0zz−10)(−−zzmzz−−)(00zf(z)m0zf(z)0limzz→f(z)=∞f(z)f(z)=mzz)(0−(z)(z)0z(0z)0m0zmf(z)0zRes[f(z),0z]jπ21∫Cdzzf)(0zf(z)C0z0zf(z)D1z2znzCD∫Cdzzf)(jπ2∑=nk1Res[f(z),kz]0zf(z)Resf(z)0z0limzz→(z-0z)f(z)0zf(z)m5Res[f(z)0z]=)!1(1−m0limzz→11−−mmdzd{(z-0z)mf(z)}f(z)=P(z)/Q(z)P(z)Q(z)0zP(0z)≠0,Q(0z)=0,)(0zQ′≠00zf(z)Res[f(z)0z]=P(0z))(0zQ′Res[f(z)]=Res[2/)/1(zzf,0]f(z)f(z)Res[f(z),]+∑=nk1Res[f(z),kz]0w=(az+b)/(cz+d)(ad-bc≠0)abcdz1z2z3zw1w2w3wkz(k=1,2,3)kw(k=1,2,3)21−−2313−−21zzzz−−2313zzzz−−()PΩ(0PΩ)Pα()SΩSαPαSαdB()Pα=-20lg|)(PajHΩ,Sα=-20lg)(SajHΩ)(sHa|)(ΩjHa|2)(sHa|)(sHa||)(ΩjHd|6(Butterworth)=0|)(ΩjHa|2=1/[1+(CΩΩ/)N2]N|)0(jHa|,|)(CajHΩ|=1/2,CΩ3dB|)(ΩjHa|2s)(sHa)(sHa−=1/[1+(CjsΩ/)N2]2NPs=(-1)N2/1(CjΩ)=CΩ]2/)12()2/1[(NPje++π2NsCΩ)(sHa)(sHa=NCΩ/∏−=−10)(NPPssCΩN,)(sHaPΩSΩPαSαλ=SΩ/PΩ,k=1101101.01.0−−SPαα,Nλlglgk3dBCΩ1+(CPΩΩ/)N2=Pα1.0101+(CSΩΩ/)N2=Sα1.0103dB)(sHa=1/∏−=Ω−Ω10)(NPCPCss)(sHass/CΩ)(sHa(Chebyshev)|)(ΩjHa|2=1/[1+)/(22CNCΩΩε]0ε1,CΩΩ/CΩ)(xCNN)(xCN=⎩⎨⎧−−)()coscos(11xNchchxN1||1||≥≤xx)(0xC=1,)(1xC=x)(1xCN+)(2xxCN)(1xCN−CΩPαSΩSαNε7λ=SΩ/CΩ,k=1101101.01.0−−PSαα,Nλ11−−chkch,ε=1101.0−Pα)(sHa=1/[ε12−N∏=−Niiss1)(]is=ξsh)212sin(πNi−ξch)212cos(πNi−ξ=N1)1(1ε−sh)(sHass/CΩ)(λjG)(ηjHH(η)=G()|)(ηλf==f(η)ηH(η)=G()|ηλ/1=η3dBCΩG()H(η)η=s/CΩH(s)lΩuΩ1SΩ2SΩ20Ω=lΩuΩCΩ=uΩlΩCΩlη0ηuη1Sη2Sη=ηηη/)(202−)(λjGH(s)=G(p)|)(202lusspΩ−ΩΩ+=p=j=)/(202ηηη−G(p)p=j|H(s)|=|G(p)|202Ω+Ω=sspC