PCM Lab

Data Communication, Lecture 5. Sample a signal, quantise the samples, encode them as bits, and send them as a digital signal.

Original (blue), samples (dots), what the receiver rebuilds (orange)

Is the sampling rate high enough?

Nyquist rate 2f Frequency the receiver sees

Below the Nyquist rate the samples fit a slower, false wave: aliasing. Try f = 5 Hz with fs = 6, 9, 10 and 12.

Signal, samples (red), quantised values (orange), level boundaries (dashed)

PCM step by step

Levels L = 2ⁿ Step Δ = (Vmax − Vmin)/L Max error Δ/2 Theory SQNR 6.02n + 1.76
Signal (blue) and delta-modulation staircase (orange) · orange shading = slope overload
Transmitted bits: 1 = step up, 0 = step down

One bit per sample

Small steps track slowly: on steep slopes the staircase falls behind (slope overload). Large steps jitter on flat parts (granular noise).

PCM bit rate and bandwidth

fs = 2 × fmax · bit rate = fs × n × channels · minimum bandwidth ≈ bit rate / 2 = n × fmax per channel.

Step 1 · Sample the analog signal
Step 2 · PAM: flat-top pulses at the sample heights
Step 3 · Quantise: each pulse moved to the middle of its level, with its code
Step 4 · Encode and send: the bit stream as a digital signal

Analog signal to digital signal

Range and step Bits sent Bit rate (Ts in s)

Lecture 6 replaces these simple two-level rules with better line codes such as NRZ-I, Manchester and AMI.