Final answer:
The total power of an FM signal across a 50 Ω antenna can be calculated using the RMS voltage and the resistance of the antenna, yielding P = (1000 / √2)² / 50 Ω.
Step-by-step explanation:
To find the total power measured across a 50 Ω antenna due to an FM signal φFM(t) =1000cos(10πⁱ10⁷t + 0.25sin(4πⁱ10⁴t)), we need to consider that the power P can be calculated using the formula P = V²/R, where V is the RMS voltage across the antenna and R is the resistance of the antenna. This FM signal can be treated as a pure tone for which the RMS voltage is equal to the peak voltage (V_peak) divided by √2, assuming a sinusoidal signal. However, note that the signal provided is already in the peak form (amplitude of 1000). Thus, the RMS voltage (V_rms) is 1000 / √2. The total power P across the 50 Ω antenna is therefore P = (V_rms)² / R = (1000 / √2)² / 50 Ω.