5.18. Ejercicios

158 5. Muestreo de señalesProcesamiento discreto de señales continuasdominio frecuencial ( f ) dominio temporal dominio frecuencial (Ω)X c ( f ) x c (t) X c (Ω)h iX(e jω ) = T∑1 X Fs c 2π (ω−2πk)kx[n] = x c (t)| t=nTX(e jω ) = T∑1 X 1 c T (ω−2πk)kY(e jω ) = H(e jω )X(e jω ) y[n] = h[n] ∗ x[n] Y(e jω ) = H(e jω )X(e jω )Y s ( f ) = Y(e jω )| ω= f 2πFs= f 2πTy s (t) = ∑y[n]δ(t−nT)nY s (Ω) = Y(e jω )| ω=Ω 2πΩs =ΩTY r ( f ) = H r ( f )Y s ( f ) y r (t) = ∑ ny[n]h r (t−nT) Y r (Ω) = H r (Ω)Y s (Ω)= TH(e jω )X(e jω )| ω= f 2π =Fs∑ ny[n] sinc t−nT T= TH(e jω )X(e jω )| ω=Ω 2πΩs= f 2πT=ΩT8>:H(e jω )| ω= f 2πFs= f 2πTsi | f | < F s2si | f | > F s28>:H(e jω )| ω=Ω 2πΩs=ΩTsi |Ω| < Ω s2si |Ω| > Ω s2Procesamiento continuo de señales discretasdominio frecuencial ( f ) dominio temporal dominio frecuencial (Ω)X c ( f ) = TX(e jω )| ω= f 2πFsx c (t) = ∑ nx[n]h r (t−nT) X c (Ω) = TX(e jω )| ω=ΩTY c ( f ) = H c ( f )X c ( f ) y c (t) = h r (t) ∗ x c (t) Y c (Ω) = H c (Ω)X c (Ω)Y(e jω ) = 1 T Y c( f )| f =ωFs2πy[n] = y c (t)| t=nTY(e jω ) = 1 T Y c(Ω)| Ω=ωΩs2π = ω TH(e jω ) =H c ( f )| f =ωFs , |ω| < π H(e jω ) = H c (Ω)| Ω=ω2πT, |ω| < πProcesamiento Digital de Señales U.N.S. 2011