Final answer:
The upper sideband frequencies of the DSB-SC AM signal are 1020 Hz and 1032 Hz, and the lower sideband frequencies are 980 Hz and 968 Hz. The total transmitted power for the given modulated signal is 23.2 watts.
Step-by-step explanation:
The student is asking about the frequencies of the upper and lower sideband components and the total transmitted power of a Double Sideband-Suppressed Carrier (DSB-SC) amplitude modulated signal.
The carrier signal is c(t) = 40 cos(2000πt), implying a carrier frequency of 1000 Hz. The message signal is m(t) = 3 cos(40πt) + 7 sin(64πt), which consists of two components with frequencies of 20 Hz and 32 Hz, respectively.
The upper sideband frequencies are obtained by adding the message signal frequencies to the carrier frequency. Thus, they are 1020 Hz (1000 Hz + 20 Hz) and 1032 Hz (1000 Hz + 32 Hz). Conversely, the lower sideband frequencies are obtained by subtracting the message signal frequencies from the carrier frequency, resulting in 980 Hz (1000 Hz - 20 Hz) and 968 Hz (1000 Hz - 32 Hz).
To calculate the total transmitted power in DSB-SC modulation, we use the formula P = Ac²/2 * (Mp²/2), where Ac is the amplitude of the carrier and Mp is the peak amplitude of the message signal. In this case, the power is purely due to the message signal as DSB-SC doesn't transmit the carrier. Therefore, P = (40²/2) * ((√(3² + 7²))²/2) = 800 * (58/2), resulting in a total power of 23.2 W.