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Question

# A low pass analog signal with bandwidth of 20 kHz is sampled at nyquist rate and quantized using a 16-level uniform quantizer. The resultant digital signal is transmitted using M-ary PSK with raised cosine pulse (roll-off factor 0.3) shaping of baseband data. If the channel bandwidth available to transmit the M-ary PSK signal is 110 kHz. then the minimum value of M required is________.4

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Solution

## The correct option is A 4fm=20kHz fs=2fm=40kHz n=log2(L)=log2(16)=4bits/symbol Bit rate, Rb=nfs=160kbps Bandwidth of baseband data modelled using raised cosine pulse is, (BW)baseband=Rb2(1+α) Bandwidth of M-ary PSK signal (for the given modelling of baseband date) is, BT=2(BW)basebandlog2M=Rb(1+α)log2M For proper signal transmission, BT≤channelBW So, Rb(1+α)log2M≤110kHz log2M≥160(1+0.3)110 Log2M≥1.89 M≥21.89 M≥3.7 So, Mmin=4

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