A PAM telemetry system involves the multiplexing of four input signals: s_i (t), i = 1, 2 3, 4. Two of the signals s₁ (t) and s₂ (t) have bandwidths of 80 Hz each, whereas the remaining two signals s₃ (t) and s₄ (t) have bandwidths of 1 kHz each. The signals s₃ (t) and s₄ (1) are each sampled at the rare of 2400 samples per second. This sampling rate is divided by 2^R (i.e., an integer power of 2.) to derive the sampling rate for s₁ (t) and s₂ (1).

(a) Find the maximum value of R.

(b) Using the value of R found in part (a), design a multiplexing system that first multi-plexes s₁ (t) and s₂ (t) into a new sequence, s₅ (t), and then multiplexes s₃ (t), s₄ (t), and s₅ (t).