1. A carrier waveform c(t) = 100cos(2π10⁸t) is frequency modulated by the message tone m(t) = 10cos(2π10⁴t).

The maximum frequency deviation is 20 kHz. Find the following:

a) The amplitude and the frequency of all signal components that have power level of at least 15% of the power of the FM signal.

b) What is the bandwidth of the FM signal?

2. Starting with the equation shown below for a SSB modulated wave, find the output produced by the coherent detector shown in the figure in response to this modulated wave. Simplify and state the bandwidth of the low-pass filter. Discuss the impact on the output of the local oscillator reference phase shift Φ.

3. Consider a system of the type shown below. Let the input signal be

x(t) = 2cos (10πt) + cos(20πt).

Sketch the spectrum of the signal at every point in the system.

4. An AM transmission system with modulation percentage 20% has a message signal of the form m(t) = 4cos(t) applied to it.

a) What are the minimum and maximum voltage levels of the envelope?

b) How much power is used on the carrier? How much power is used for the message (the sidebands)?

c) We would like to use an envelope detector to demodulate this signal. Will the signal be distorted? What are two things that we can do to reduce distortion.