Final answer:
For the signal x1(t) = 2cos(20πt + π/3), the average power is 2 watts and the power spectral density consists of delta functions at ±10Hz.
Step-by-step explanation:
The question is related to the concept of power spectral density (PSD) and average power in an electrical engineering and signal processing context. For the given signal x1(t) = 2cos (20πt + π/3), the average power can be computed using the formula P = (1/2)A2, where A is the amplitude of the signal.
In this case, A = 2, thus P = (1/2)(2)2 = 2 watts. The power spectral density for a pure sinusoid is represented as a pair of Dirac delta functions at positive and negative frequencies of the sinusoid (in this case ±10Hz). Therefore, the PSD is concentrated at these two frequencies with the respective magnitude.