Analogue-to-digital conversion: sampling rate and the Nyquist theorem, aliasing and the anti-aliasing filter, bit depth and quantisation, dynamic range and quantisation noise, and common audio resolutions.

What this dot point is asking

Edexcel wants you to explain how a continuous analogue waveform becomes digital data, and what the two key parameters control. Sampling rate sets how often the amplitude is measured (and therefore the highest frequency that can be captured, via Nyquist); bit depth sets how finely each measurement is stored (and therefore the dynamic range). You must also explain aliasing and quantisation. This is examined with short calculations in Component 3.

The answer

Analogue-to-digital conversion

The result is a set of discrete points that approximate the original curve. The closer together the samples (higher rate) and the finer the levels (higher bit depth), the more faithfully the digital version represents the analogue original.

Sampling rate and the Nyquist theorem

Because the ear hears up to about $20$ kHz, audio must be sampled at least $40$ kHz. CD audio uses $44.1$ kHz (Nyquist frequency $22.05$ kHz), and $48$ kHz is standard for video; higher rates such as $96$ kHz and $192$ kHz are used in production for extra margin. The small gap above $40$ kHz gives the anti-aliasing filter room to work.

Aliasing

Aliasing is why you cannot just sample slowly and hope for the best, and why digital synthesis and sample-rate conversion must be done carefully. The filter is the safeguard that keeps the captured band clean.

Bit depth and quantisation

The rounding in quantisation introduces a small error heard as quantisation noise, worst on quiet passages where the signal uses few levels. Higher bit depth lowers this noise floor, which is why production is done at $24$-bit even though the final master may be reduced to $16$-bit for CD.

Common resolutions

CD is $44.1$ kHz / $16$-bit. Professional recording is typically $48$ kHz or $96$ kHz at $24$-bit. The file size grows with both parameters, so a higher rate and depth trade storage and processing load for fidelity and headroom.

Examples in context

When you set a session to $48$ kHz / $24$-bit, you are choosing to capture the full audible band with generous headroom and a low noise floor. When you down-sample a project for streaming, an anti-aliasing filter must remove the now out-of-band content first. When a cheap converter sounds harsh, poor anti-aliasing or low bit depth may be adding aliasing or quantisation noise. The principles of sampling and quantisation explain the quality of every digital recording you make.

Try this

Q1. State the Nyquist theorem in one sentence. [1 mark]

• Cue. The sampling rate must be at least twice the highest frequency in the signal.

Q2. A signal contains frequencies up to $15$ kHz. Find the minimum sampling rate. [2 marks]

• Cue. $f_s \ge 2 \times 15 = 30$ kHz.

Q3. State the approximate dynamic range of a $16$-bit recording. [2 marks]

• Cue. $16 \times 6 \approx 96$ dB.