In QAM [8], it is possible to send two signals on a single channel, which effectively do...

In QAM [8], it is possible to send two signals on a single channel, which effectively doubles the bandwidth of the channel. QAM is used in the uplink (path from the house to the service provider) in today’s 56,000 bits/second modems, in DSL modems, and in Motorola‘s Nextel cellular phones.

A block diagram of a QAM system is shown in Figure P6.30. Assume that f₁(t) and F₂(t) have bandwidth is the carrier frequency.

You will find the trigonometric identities in Appendix A useful for solving this problem.

We form the following signals, as shown in Figure P6.30:

(a) Determine the signal g₁(t).

(b) Determine the signal g₂(t).

(c) As shown in Figure P6.30, g₁(t) and g₂(t) are filtered by ideal low-pass filters, with cutoff frequency of 2w₀ and unit amplitude, to form the output signals e₁(t) and e₂(t). Determine e₁(t) and e₂(t).