Can you solve the following problem and show how the answer was found:

A17)

Using Carson's rule, determine the transmission bandwidth for commercial FM radio broadcasting, provided that the maximum value of frequency deviation is 75 kHz and the bandwidth of the audio signal is 15 kHz

2. Laboratory Preliminary Discussion First-order High-pass RC Filter Analysis The first-order high-pass RC filter shown in figure 3 below represents all voltages and currents in the time domain. We will again convert the circuit to its s-domain equivalent as shown in figure 4 and apply Laplace transform techniques. ic(t) C vs(t) i₁(t) + + vc(t) R1 ww Vi(t) || 12(t) V2(t) R₂ Vout(t) VR2(t) = V2(t) Figure 3: A first-order high-pass RC filter represented in the time domain. Ic(s) C + Vs(s) I₁(s) + + Vc(s) R₁ www V₁(s) 12(s) V₂(s) R₂ Vout(S) = VR2(S) = V2(s) Figure 4: A first-order high-pass RC filter represented in the s-domain. Again, to generate the s-domain expression for the output voltage, You (S) = V2 (s), for the circuit shown in figure 4 above, we can apply voltage division in the s-domain as shown in equation 2 below. Equation 2 will be used in the prelab computations to find an expression for the output voltage, xc(t), in the time domain. equation (2) R₂ Vout(s) = V₂(s) = R₂+…

Can you show me the steps to get the last part after the second equal sign.

Prelab Information 1. Laboratory Preliminary Discussion First-order Low-pass RC Filter Analysis The first-order low-pass RC filter shown in figure 1 below represents all voltages and currents in the time domain. It is of course possible to solve for all circuit voltages using time domain differential equation techniques, but it is more efficient to convert the circuit to its s-domain equivalent as shown in figure 2 and apply Laplace transform techniques. vs(t) i₁(t) + R₁ ww V₁(t) 12(t) Lic(t) Vout(t) = V2(t) R₂ Vc(t) C Vc(t) VR2(t) = V2(t) + Vs(s) Figure 1: A first-order low-pass RC filter represented in the time domain. I₁(s) R1 W + V₁(s) V₂(s) 12(s) Ic(s) + Vout(S) == Vc(s) Vc(s) Zc(s) = = VR2(S) V2(s) Figure 2: A first-order low-pass RC filter represented in the s-domain.

A.15 Consider a communication channel, transfer characteristic of which is defined by the nonlinear relation, y(t) = x(t) + x² (t), where x(t) is the input and y(t) is the output. Assuming the input is an FM signal, x(t) = cos (2лft+(t)), find y(t). Is it possible to retrieve x(t) from y(t)? If so, how?

1) Show that a regenerative receiver can be used to recover message from the following modulated signals. a. DSB-PC b. DSB-SC 1b) Does the receiver need to recover the carrier phase? 1c) What are the filtering requirements and restrictions on message signal bandwidth and carrier frequency.

2) Estimate the transmission bandwidth for the following FM modulated signals (W is the message bandwidth) a) W1KHz and frequency deviation of 75KHz b) W = 20KHz and frequency deviation of 75KHz c) W1KHz and frequency deviation of 150KHz d) W20KHz and frequency deviation of 150KHZ