Four signals having bandwidths $1,2,2,4$ kHz respectively are sampled and TDM multiplexed. The TDM signal is PCM encoded using a $4-$bit PCM encoder. a$)$ Construct a TDM commutator showing the number of nodes for each signal and the frequency of rotation. b$)$ Find the bit rate of this TDM system. c$)$ What is the minimum null bandwidth required to transmit this TDM signal using a pulse shape. d$)$ What is the minimum null bandwidth required to transmit this TDM signal using a rectangular pulse shape. $$