Pulse code modulation.

The idea

Pulse code modulation (PCM) converts a continuously varying analogue signal into a digital bitstream. The analogue voltage is sampled at regular intervals at the sampling frequency; each sample is quantised by rounding to the nearest available level on a fixed scale; each level is then assigned a binary code, and the codes are transmitted as pulses. A higher sampling rate and more quantisation levels give a closer copy of the original but need more bits per second. For example, a 2 V signal sampled at 8 kHz with 256 levels uses 8 bits per sample, giving 64 kbit/s. The receiver decodes each binary word back to a voltage and reconstructs an approximation of the original waveform.

What earns the marks

• Sampling: the analogue signal is measured at regular time intervals, with the sampling frequency determining how often samples are taken.
• Quantisation: each sample value is rounded to the nearest discrete level on a fixed amplitude scale, introducing quantisation error.
• Encoding: each quantisation level is represented by a binary code, and the sequence of codes is transmitted as pulses.
• Bit rate: bit rate equals samples per second multiplied by bits per sample, so more levels or a higher sampling frequency increase the data rate.
• Reconstruction: the receiver converts each binary word back to a voltage level and outputs a stepped approximation of the original signal.
• Fidelity: increasing sampling frequency and the number of quantisation levels reduces distortion and quantisation error but increases bandwidth or storage needs.

Common mistakes and how to put them right

• Confusing sampling with quantisation.

  Put it right: Sampling fixes the times at which values are read, while quantisation fixes the amplitude values available; state both stages separately.

• Believing that a digital copy is exact.

  Put it right by explaining quantisation error.

• Forgetting that bit rate depends on both sampling frequency and bits per sample.

  Put it right by using bit rate = sampling frequency × bits per sample.

Exam tips

• Define each stage in order — sampling, quantisation, encoding, transmission and reconstruction — so the whole process is clear.
• Use a numerical example, such as 8 kHz sampling with 8 bits per sample giving 64 kbit/s, to show how bit rate is calculated.
• When comparing PCM with analogue transmission, refer to noise immunity, regeneration of pulses and the trade-off between quality and data rate.