Section 18.6 Applications

18.58 An AM signal is specified by

f (t) = 10(1 + 4 cos 200πt) cos π× 104 t

Determine the following:

(a) the carrier frequency,
(b) the lower sideband frequency,
(c) the upper sideband frequency.
18.59 For the linear system in Fig. 18.54, when the input voltage is vi(t) = 2δ(t) V, the output is vo(t) = 10e⁻2*^t* − 6e⁻4*^t* V. Find the output when the input is vi(t) = 4e⁻^t u(t) V.

Figure 18.54 For Prob. 18.9.

18.60 A band-limited signal has the following Fourier series representation:

is(t) = 10 + 8 cos(2πt + 30°) + 5 cos(4πt − 150°)mA

If the signal is applied to the circuit in Fig. 18.55, find v(t).

Figure 18.55 For Prob. 18.60.

18.61 In a system, the input signal x(t) is amplitudemodulated by m(t) = 2 + cosω0t. The response y(t) = m(t)x(t). Find Y(ω) in terms of X(ω).

18.62 A voice signal occupying the frequency band of 0.4 to 3.5 kHz is used to amplitude-modulate a 10-MHz carrier. Determine the range of frequencies for the lower and upper sidebands.
18.63 For a given locality, calculate the number of
stations allowable in the AM broadcasting band (540–1600 kHz) without interference with one another.
18.64 Repeat the previous problem for the FM broadcasting band (88–108 MHz), assuming that the carrier frequencies are spaced 200 kHz apart.
18.65 The highest-frequency component of a voice signal is 3.4 kHz. What is the Nyquist rate of the sampler of the voice signal?
18.66 A TV signal is band-limited to 4.5 MHz. If samples are to be reconstructed at a distant point, what is the maximum sampling interval allowable?
18.67 Given a signal g(t) = sinc(200π t), find the Nyquist rate and the Nyquist interval for the signal. *