How it works
PCM consists of three steps: sampling at f_s ≥ 2f_max (Nyquist), quantisation into 2ⁿ levels with quantisation noise power σ_q² = Δ²/12 where Δ = V_range/2ⁿ is the step size, and binary encoding of each level into an n-bit word. Bit rate R_b = n·f_s bits/second. Quantisation SNR for uniform PCM = 6.02n + 1.76 dB — each additional bit improves SNR by approximately 6 dB, so 8-bit PCM gives about 49.9 dB SNR and 16-bit audio gives 98.1 dB.
Key points to remember
Quantisation error ranges from −Δ/2 to +Δ/2, modelled as uniformly distributed noise with power Δ²/12. Non-uniform quantisation (companding) uses smaller steps for small amplitudes and larger steps for large amplitudes — µ-law companding (µ=255 in North America) and A-law (A=87.6 in Europe/India) are the two standards. Companding improves SNR for low-amplitude signals (typical speech) by about 40 dB over uniform PCM. Differential PCM (DPCM) encodes only the difference from the predicted value, reducing bit rate. ADPCM (32 kbps) is used in ISDN voice channels and reduces the 64 kbps PCM rate by half.
Exam tip
Every Anna University paper asks you to calculate bit rate and quantisation SNR for a given number of bits and sampling rate — apply the 6.02n + 1.76 dB formula directly and show that increasing n by 1 always adds ≈ 6 dB to SNR.