Principles of Communication Engineering

Answer

Correct Option: (i) Companding

Explanation

Companding ($\mu$-law/A-law compress-expand) non-uniform quantization: small amplitudes fine steps, large coarse. Reduces quantization noise for small signals, improves SQNR vs uniform PCM. Differential PCM and Delta Modulation also reduce but companding is standard for PCM noise reduction.

Final Answer

Companding → Option (i).

Answer

DPCM: Quantize difference $d[n]=x[n]-\hat{x}[n]$, predictor $\hat{x}=a_1\tilde{x}[n-1]$. Block $x$→subtract predictor→Quantizer→Encoder→Channel→Decoder→predictor loop. Variance of $d$ << variance of $x$ → fewer bits, prediction gain $G_p=\sigma_x^2/\sigma_d^2$. Better SNR for correlated speech/video vs PCM.

Answer

Slope overload condition: $|dm/dt|_{max}\le\Delta f_s$. For $m=A_m\cos\omega_m t$, $|dm/dt|_{max}=A_m\omega_m$. So $f_m\le\Delta f_s/(2\pi A_m)$. Given $\Delta=0.1$V $f_s=10$kHz $A_m=1$V → $f_{max}=159$Hz. General $f_{max}=\Delta f_s/(2\pi A_m)$.

Answer

DPCM block: $x[n]$→subtract predictor→Quantizer→Encoder→Channel→Decoder→predictor loop. $e[n]=x[n]-\hat{x}[n]$, $\tilde{x}=\hat{x}+e_q$. Exploits correlation, fewer bits. See Q45.

Answer

ADM: Adaptive step $\Delta[n+1]=\Delta[n]\cdot K$ if consecutive bits same (slope overload) increase, if alternating decrease. Handles steep and flat. SNR +10dB vs DM, wider dynamic range.