Analogue-to-digital conversion: sampling audio signals for transmission in…

The idea

Analogue-to-digital conversion turns a continuously varying voltage into a sequence of binary numbers. The analogue signal is sampled at regular intervals at a chosen sampling rate, and each sample is quantised by comparing it with a set of discrete voltage levels encoded using two voltage levels, high and low, representing 1 and 0. More bits per sample give more levels and smaller steps, while a higher sampling rate captures faster changes. Digital transmission allows the original data to be recovered from a noisy signal because the receiver only needs to distinguish the two voltage levels, so moderate noise does not change the decoded bits. However, sampling loses information between samples and quantisation introduces an error, so the recovered signal is an approximation.

What earns the marks

• Sampling measures the analogue voltage at regular time intervals; the sampling rate is the number of samples taken per second, measured in hertz.
• Quantisation assigns each sample to the nearest available discrete level, and the number of levels is 2ⁿ where n is the number of bits per sample.
• Digital data is represented using two voltage levels, one for binary 1 and one for binary 0, so the signal is a sequence of pulses rather than a continuous voltage.
• Increasing the sampling rate reduces the time between samples and allows faster variations in the analogue signal to be represented.
• Increasing the number of bits per sample reduces the voltage step between adjacent levels, lowering quantisation error and improving fidelity.
• In a noisy communication system, digital pulses can still be identified as 1 or 0 provided the noise does not push a level past the decision threshold, so the original data can be recovered and regenerated.

Common mistakes and how to put them right

• Confusing sampling rate with bit depth.

  Put it right by stating that sampling rate is about how often measurements are taken in time, while bit depth is about how many levels each measurement can take.

• Believing that digital signals are completely immune to noise.

  Put it right by explaining that noise can still corrupt bits if it is large enough to cross the decision threshold.

• Thinking that a higher sampling rate alone removes quantisation error.

  Put it right by noting that quantisation error depends mainly on the number of bits per sample.

• Describing the two voltage levels as analogue values rather than as the binary states 1 and 0.

  Put it right by linking each level to one bit value.

Exam tips

• Use the phrase number of bits per sample when discussing resolution, and sampling rate when discussing how often samples are taken, so the two effects are not mixed up.
• When explaining noise resistance, refer to the receiver distinguishing two voltage levels rather than to the signal being unchanged.
• Include one advantage and one disadvantage of digital sampling when the question asks for a comparison, and support each with a physical reason.
• Sketch or describe the staircase shape produced by quantisation to show how the digital approximation differs from the smooth analogue input.