Signals and Systems - Electrical Engineering

384 C H A P T E R 6: Application to Control and Communications m 1 (t) m 2 (t) m 2 (t) s(t) r(t) cos(Ωct) × + LPF LPF π 2 shift ...

6.4 Application to Communications 385 + Channel m 1 (t) m 2 (t) × × × cos(Ω 1 t) cos(Ω 2 t) cos(Ω 3 t) cos(Ω 1 t) cos(Ω 2 t) cos ...

386 C H A P T E R 6: Application to Control and Communications c(rad/sec) withm(t), the transmitted signals(t)in angle modulati ...

6.4 Application to Communications 387 Using the spectrum of a cosine and the modulation theorem, we get S()≈π[δ(−c)+δ(+c)]− ...

388 C H A P T E R 6: Application to Control and Communications 0 0.05 0.1 0.15 0.2 − 50 0 50 m (t) 0 0.05 0.1 0.15 0.2 −0.5 0 0. ...

6.4 Application to Communications 389 0 0.02 0.04 0.06 0.08 0.1 − 50 0 50 m (t ) − 200 − 150 − 100 − (^50050100150200) 0 5 10 |M ...

390 C H A P T E R 6: Application to Control and Communications 6.5 Analog Filtering The basic idea of filtering is to get rid of ...

6.5 Analog Filtering 391 Magnitude Squared Function The magnitude-squared function of an analog low-pass filter has the general ...

392 C H A P T E R 6: Application to Control and Communications FIGURE 6.22 Magnitude specifications for a low-pass filter. Ω Ω 1 ...

6.5 Analog Filtering 393 Factorize the magnitude-squared function and choose the poles on the left-hand s-plane, guaranteeing t ...

394 C H A P T E R 6: Application to Control and Communications we letH(S)= 1 /D(S)—that is, we assign toH(S)the poles in the lef ...

6.5 Analog Filtering 395 Thus, the desired filter with a dc gain of 10 is obtained by multiplyingH(S)by 10. Furthermore, if we l ...

396 C H A P T E R 6: Application to Control and Communications Remarks n According to Equation (6.43) when either n The transiti ...

6.5 Analog Filtering 397 definition is used. Likewise, whenever|′|≤1, the definition based in the hyperbolic cosine would not b ...

398 C H A P T E R 6: Application to Control and Communications n Different from the Butterworth filter that has a unit dc gain, ...

6.5 Analog Filtering 399 where the last term is the definition of the Chebyshev polynomial for ′ hp>1. Thus, we get hp=pco ...

400 C H A P T E R 6: Application to Control and Communications the filter is analog by including an ’s’ as one of the arguments. ...

6.5 Analog Filtering 401 H = num/den; % frequency response Y = X∗H; % convolution property y = ifourier(Y, t); % inverse Fourier ...

402 C H A P T E R 6: Application to Control and Communications − 8 − 6 − 4 − 2 0 2 − 5 0 5 Butterworth σ σ − 4 − 2 0 2 − 5 0 5 C ...

6.5 Analog Filtering 403 basic filters are given by: Low pass-low pass: S= s  0 Low pass-high pass: S=  0 s Low pass-band pass ...