A signal x1(t) is bandlimited to 3kHz. There are three more signals x2(t),x3(t) and x4(t) which are bandlimited to 1kHz each. These signals are tobe transmitted by a TDM systemi. Design a TDM scheme where each signal is sampled at its Nyquistrate.ii. What must be the speed of commutator?iii. Calculate the minimum transmission bandwidth of channel.

To design a TDM scheme for transmitting the given signals, we need to follow the following steps:

i. Sampling at Nyquist rate: Since each signal is bandlimited, we need to sample each signal at its Nyquist rate to avoid aliasing. The Nyquist rate is twice the bandwidth of the signal.

For signal x1(t) with a bandwidth of 3kHz, the Nyquist rate would be 6kHz. For signals x2(t), x3(t), and x4(t) with a bandwidth of 1kHz each, the Nyquist rate would be 2kHz for each signal.

ii. Speed of commutator: The speed of the commutator determines the rate at which the samples of each signal are transmitted. In TDM, the commutator switches between the samples of different signals at a constant rate.

To determine the speed of the commutator, we need to consider the highest Nyquist rate among all the signals. In this case, the highest Nyquist rate is 6kHz for signal x1(t).

Therefore, the speed of the commutator should be set at 6kHz to accommodate the highest Nyquist rate.

iii. Minimum transmission bandwidth: The minimum transmission bandwidth of the channel can be calculated by adding up the bandwidths of all the signals being transmitted.

In this case, we have four signals:

• Signal x1(t) with a bandwidth of 3kHz
• Signals x2(t), x3(t), and x4(t) with a bandwidth of 1kHz each

Adding up these bandwidths, we get: 3kHz + 1kHz + 1kHz + 1kHz = 6kHz

Therefore, the minimum transmission bandwidth of the channel should be 6kHz to accommodate all the signals.