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.
![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)
![The following figure shows a switching modulator. Assume the lowpass message signal m(t) has bandwidth 3000 Hz and max|m(t)| = 0.2. The carrier signal is c(t) = cos(2π15000 t). x(t) = m(t)+c(t). After the diode, the signal y(t) is periodic and thus its Fourier series representation is y(t) = x(t)[12+2πcos(2π15000 t)−23πcos(2π3×15000 t)+25πcos(2π5×15000 t)−⋯]. (1) With an appropriate bandpass filter BPF, this modulator can conduct AM modulation. Please determine the magnitude spectrum of the ideal BPF (e. g. , determine its center frequency and bandwidth). Find the output AM signal waveform expression s(t) and its percentage modulation. (2) Can it work as a DSB-SC modulator? If yes, please also find the appropriate magnitude spectrum of the ideal BPF and find the output DSB-SC signal waveform expression s(t).](https://www.doubtrix.com/uploads/editor/1706063044cSWEkzuDjS.jpeg)
![(a) An AM signal is given by φAM(t) = [20 + m(t)]cos(2πfct). Find the maximum value of the amplitude Am of the modulating signal m(t), as shown in the following figure, such that no distortion in the modulated signal would occur. Find also the corresponding modulation index. The figure for Problem 01 . (b) A baseband signal is given by m(t) = cos100t cos200t and the carrier signal is given by C(t) = 10cos5000t. Find and sketch the spectra of the DSB-SC modulated signal. Find also the upper sideband and the lower sideband. (c) What is the major drawback of SSB-SC and how can we overcome it?](https://www.doubtrix.com/uploads/editor/8592024853PjFUzTsBBt.png)