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Problem 1 (Pulse Code Modulation) In a PCM scheme, a uniform quantizer with 2" quantization levels is used to quantize the source samples, where v is the number of bits per sample, which is an integer

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Problem 1 (Pulse Code Modulation) In a PCM scheme, a uniform quantizer with 2" quantization levels is used to quantize the source samples, where v is the number of bits per sample, which is an integer. The signal X(t) is a stationary random process with an auto-correlation function given by RX(T) A2 2 e cos 27 fot We know that the random process never exceeds 4 in magnitude. Assume that A = 4. (a) How many quantization levels (N = 2”) are required to guarantee an SQNR of at least 40 dB? (b) Assuming that the signal is quantized to satisfy the condition of Part (a) and assuming the approximate bandwidth of the signal is W, what is the minimum required channel bandwidth for the transmission of a PCM signal based on this quantization scheme? Problem 2 (Pulse Code Modulation) A signal can be modeled as a low-pass stationary process X(t), whose probability density function (PDF) at any time t is given by s (x+3) fx(x) = (3 – x) -3