Final answer:
The output signal of the low-pass filter, after multiplying by cos(2πfεt + θ), is a low-frequency component closely related to the original baseband signal m(t), provided that fε is approximately equal to the carrier frequency fc and with an appropriate choice of θ.
Step-by-step explanation:
In the process of demodulation of a frequency-translated signal, the baseband signal m(t) is recovered through mixing and filtering. When the signal v(t)=m(t) cos 2πfct is multiplied by cos(2πfεt + θ), two primary components are generated, one at a low frequency and another at a high frequency (the sum frequency).
After passing through a low-pass filter, which rejects frequencies higher than its cutoff frequency, the high-frequency component is removed, and the remaining output is closely related to the original baseband signal m(t). If the frequencies fc and fε are close, such that fε ≈ fc, and θ is selected appropriately (i.e., θ = 0 or θ = π), the output will primarily be a scaled version of m(t) possibly with a phase shift depending on θ. However, if there is a significant difference between fc and fε, additional signal processing may be required to recover m(t).