$($a$)$ With suitable examples and diagrams, explain the relation between ASK, PSK$,$ QAM.$($b$)$ A telephone line having a bandwidth of $0-4000$ Hz is to be used for transmitting voice samples limited to $3000$ Hz with $7$ bits per sample. Without compression, what will be the acceptable SNR and the required bits per transmission symbol?$($c$)$ With an example, explain the working of code division multiplexing, including its orthogonality and spread spectrum characteristics.$($d$)$ For an ADSL system suppose that the channel$-$wise characterization is as follows: signal strength at source is Ss$,$ signal strength after reaching destination is Sd$,$ white noise level is Nw$,$ noise level due to cross talk is Nx per cable in bundle, number of cables in a bundle is k$.$ If noise is assumed to be additive, derive expressions for achievable upstream and downstream data transmission rates per channel; $($represent any required unknown quantity with a suitable and documented symbolic value$).($e$)$ Neatly draw the waveforms resulting from NRZ$,$ NRZ$-$I, bipolar$-$AMI, Manchester and differential Manchester encoding for transmitting the bit stream $00110110.$