PCM and baseband transmission
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| quantisation/ˌkwɒntaɪˈzeɪʃn/ | lấy mẫu |
| PCM | PCM |
| raised-cosine | hàm cos nâng cao |
From voltage to bits
- Quantisation with n bits gives $2^{n}$ levels and $SQNR \approx 6.02n + 1.76$ dB. Sampling at $f_s > 2W$ then encoding is PCM.
4 kHz voice at 8 kHz, 8 bits: 64 kbps and SQNR 49.9 dB ✓ — the telephone number.
{exercise:uni-ee1105-telephone}
A 4 kHz voice channel sampled at 8 kHz with 8 bits per sample gives —
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8000 samples/s × 8 bits = 64 kbps; SQNR = 6.02×8 + 1.76 = 49.9 dB (256 levels).
Each extra quantisation bit buys about —
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One bit doubles the levels: 10·log₁₀4 = 6.02 dB. The 1.76 is the sine-signal constant, added once.
Shaping the wire
- The raised-cosine filter trades bandwidth for timing slack: $B = (1+\alpha)R_s/2$ — 0.675 MHz at 1 Msym/s, $\alpha = 0.35$. Manchester doubles bandwidth to buy the clock line.
{exercise:uni-ee1105-cosine}
At Rs = 1 Msym/s with roll-off 0.35 the raised-cosine bandwidth is —
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B = (1+α)Rs/2 = 1.35/2 = 0.675 MHz — the datasheet number; α = 0 is the unbuildable 0.5 MHz bound.