1.

A)

Uniform quantization is to be applied to the sampled values in an encoder. Assume that 4 bits are used for encoding and that the quantizer has maximum / minimum values of 4.6. (a) What is the maximum possible quantizer error? (b) For a sampled value of 2.94, what is the quantized value after decoding, assuming no errors are introduced because of channel noise? (c) Find the quantization error for this sample and hence calculate the sample SQR in dB. (d) If Gray codewords are assigned, what is the codeword assigned to this sample value?

(e) Alternatively, if codewords are assigned decimally, what is the codeword assigned to this sample value? (In both cases, assume all-zero codeword is assigned to the most negative quantized value) (f) If the second digit of this codeword is decoded incorrectly, what is the sample error in the decoded value (i) when Gray codes are used, and (ii) when decimal codes are used?

B)

(i) A 16-level signaling scheme uses levels with a max/min of 3.2. Choose a set of levels such that the difference between neighboring levels is always the same. For the following sequence of information bits, sketch a multilevel signaling scheme using RZ pulses with a duty cycle of 50%: 0010101011110101101101001101 Assign codewords to the various levels such that a minor decoding error means we get an error in only one-bit position most of the time (ie, use a Gray code). If the symbol interval is 7.5 s, what is the symbol rate and what is the information data rate? (ii) If, for some reason, the receiving system clips all positive levels at +2.9, how many information bits are decoded incorrectly for the given sequence? (iii) On the average for any given random sequence of bits, what percentage of the bits will be decoded incorrectly because of this symbol clipping?