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The baseband signal m(t) in the frequency-translated signal v(t)=m(t) cos 2πfc t is recovered by multiplying v(t) by the waveform cos(2πfϵ t + θ).

The product waveform is transmitted through a low-pass filter which rejects the doublefrequency signal. What is the output signal of the filter?

1 Answer

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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 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 , additional signal processing may be required to recover m(t).

User Michael Petito
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