JNTU B.Tech III DIGITAL COMMUNICATIONS Previous Question Paper (September 2021 - R16)

Differential Pulse Code Modulation (DPCM) is a technique where the difference between the current sample value and its predicted value is quantized and transmitted. The system consists of a predictor and a quantizer. The predictor estimates the current sample based on previous samples, and the error signal (difference between actual and predicted value) is quantized to reduce redundancy.

Slope overload noise occurs in predictive systems when the input signal changes faster than the system can track. If the input signal x(t) has a maximum slope of x'(t) and the system step size is Δ with sampling period T_s, the condition for no slope overload is:

If the input signal exceeds this rate, the predictor cannot keep up, leading to a tracking error that grows linearly. The slope overload noise power is proportional to the square of the difference between the signal slope and the maximum tracking slope of the system.

Quantization is the process of mapping a continuous amplitude signal into a finite set of discrete levels. For a uniform quantizer with a total range of V volts and L levels, the step size is Δ = V / L. Assuming the quantization error e is uniformly distributed between -Δ/2 and +Δ/2, the mean square quantization noise power N_q is:

If the signal power is S, the Signal-to-Quantization Noise Ratio (SQNR) is given by:

For a sinusoidal signal with amplitude A, S = A^2 / 2. Substituting Δ = 2A / L, the SQNR becomes:

In decibels, this is expressed as SQNR(dB) = 1.76 + 6.02n, where n is the number of bits per sample (L = 2^n).