Analogue vs Digital Sound

Sound is a continuous analogue signal — a pressure wave that varies smoothly over time. Computers, however, can only store discrete digital values. To store sound digitally, the analogue signal must be converted to digital form using an Analogue-to-Digital Converter (ADC).

The ADC Sampling Process

Sampling is the process of measuring the amplitude (volume) of an analogue sound signal at regular time intervals and storing each measurement as a binary number.

1. Sample: At each regular time interval, the ADC measures the current amplitude of the analogue signal.
2. Quantise: The measured amplitude is rounded to the nearest available digital level.
3. Encode: The quantised value is stored as a binary number.

Key Terms

Sample Rate (Sampling Frequency)

Sample rate is the number of samples taken per second, measured in Hertz (Hz) or kHz.

• Higher sample rate → more samples per second → better reproduction of the original signal → larger file size
• CD quality: 44,100 Hz (44.1 kHz)
• Phone quality: 8,000 Hz (8 kHz)

According to the Nyquist theorem, the sample rate must be at least twice the highest frequency in the sound to reconstruct it accurately. For human hearing (up to ~20 kHz), a sample rate of ≥40 kHz is needed.

Bit Depth (Sample Resolution)

Bit depth is the number of bits used to store each sample. It determines how many different amplitude levels can be represented:

Number of amplitude levels = 2^{bit depth}

• Higher bit depth → more amplitude levels → finer detail → larger file size
• CD quality: 16 bits (65,536 levels)
• Professional audio: 24 bits

Audio File Size Calculation

File size (bits) = Sample rate × Bit depth × Duration (seconds)

For stereo (two channels), multiply by 2.

Worked Example

Calculate the file size of 3 minutes of stereo audio at 44,100 Hz sample rate and 16-bit depth:

1. Duration = 3 × 60 = 180 seconds
2. Bits = 44,100 × 16 × 180 = 126,720,000 bits
3. For stereo: × 2 = 253,440,000 bits
4. Bytes: 253,440,000 ÷ 8 = 31,680,000 bytes
5. MB: 31,680,000 ÷ 1,048,576 ≈ 30.2 MB

Quantisation Error

Because amplitude values are rounded to the nearest digital level, there is always a small difference between the true analogue value and the stored digital value. This is called quantisation error or quantisation noise. Higher bit depth reduces quantisation error.

DAC — Digital to Analogue Converter

When playing back audio, the stored digital values are converted back to an analogue signal by a Digital-to-Analogue Converter (DAC). This signal is then amplified and sent to speakers or headphones.