Consider an amplitude modulation with carrier (DSC-WC) having a modulation index of 0.5. The message signal m(t) is a periodic signal as shown in the figure. a) Sketch the modulator structure. If the carrier frequency is 5 kHz, sketch the modulated signal which is transmitted (in time domain). b) You may use envelope detector circuitry to recover the signal m(t). Draw this circuitry and explain its function.
![Question 2: In an amplitude modulation system, the message signal is given as shown below: The carrier frequency is 1 kHz and the modulator output is: s(t) = 2[b + 0.5 m(t)]cos(2πfct) a) Determine the average message power. b) If b = 1, determine the modulation index and the modulation power efficiency. c) Sketch the modulated signal s(t) = 2[b + 0.5 m(t)]cos(2πfct) in time domain if b = 1. d) Draw the detailed receiver structure and show the signals at all the stages of the receiver. e) Discuss the system, if b = 0.5.](https://www.doubtrix.com/uploads/editor/7598963780CnyAeHUsmz.png)
![P3: In an amplitude modulation system, the message signal is the periodic square wave shown below and the carrier frequency is 1 kHz. The modulator output is xAM(t) = 2[b+0.5 m(t)]cosωct (a) Determine the average power in xAM(t) as a function of b and A. (b) If b = A, determine the modulation index and the modulation power efficiency. (c) Find the minimum value of b such that the AM signal can still be demodulated via envelope detection. Determine maximum modulation index and maximum modulation power efficiency based on the resulting b.](https://www.doubtrix.com/uploads/editor/0689037952brAqHOsamN.jpg)
![An amplitude modulated wave is given by s(t) = [1 + kam(t)]c(t), where ka is the modulator sensitivity, m(t) is the message wave and c(t) is the carrier wave. Assume that a sinusoidal signal is chosen as the carrier wave; c(t) = cos(2πfct), where fc is the carrier frequency. Let the message signal m(t) be a periodic triangular pulse wave shown in Fig. 1 Figure 1: Message signal m(t) (a). Find ka for 50% modulation. [hint: Percentage modulation is defined as max|kam(t)| × 100% ] (b). Sketch the amplitude modulated signal s(t) for 50% modulation.](https://www.doubtrix.com/uploads/editor/0778063553RLzvMpgLmL.jpeg)