Let x(t) be a real-valued signal for which X(jω) = 0 when | ω | > 2,000π . Amplitude modulation is performed to produce the signal
g(t) = x(t)sin(2,000/ πt).
A proposed demodulation technique is illustrated in Figure P8.3 where g(t) is the input, y(t) is the output, and the ideal lowpass filter has cutoff frequency 2,000π and passband gain of 2. Determine y(t).
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