Final answer:
The output of the signal after filtering will only contain frequency components below 4 kHz; the carrier frequency of 100 kHz will be filtered out, leaving only the modulation frequency if it is within the passband of the filter.
Step-by-step explanation:
The student's question involves the output of a signal after passing through an ideal low-pass filter with a cut-off frequency of 4 kHz. The signal to be filtered is a product of two cosine functions, one with modulation frequency fm and the other with carrier frequency f = 100kHz. After passing through the low-pass filter, only frequencies below 4 kHz will remain, which implies that the high-frequency carrier (100kHz) will be removed. Therefore, the output signal will solely be dependent on the modulation frequency and the value of theta (θ). When θ = 0, we would see a signal identical to the modulation frequency assuming it is within the passband of the filter. For θ = π/2 or θ = π, the output would also relate to the modulation frequency as long as it is beneath the cut-off frequency of the low-pass filter. Any potential phase shift would affect the phase but not the amplitude spectrum. The amplitude spectrum would show a peak at the modulation frequency (if within the passband) with zero amplitude for frequencies beyond the 4 kHz cut-off.