Revise Multimedia - Sound for Cambridge 9618 (1.2.2)

To digitise sound, we must convert the continuous analogue wave into a series of discrete numerical values. This crucial task is performed by an Analogue-to-Digital Converter (ADC). The microphone captures the sound wave and converts it into an analogue electrical signal. The ADC then takes this signal and transforms it into a stream of binary data that the computer can understand. To play the sound, the process is reversed by a Digital-to-Analogue Converter (DAC), which turns the binary data back into an analogue signal sent to your speakers.

The core of digitisation is sampling. This involves measuring the amplitude (height) of the sound wave at very regular time intervals. The frequency at which these samples are taken is called the sampling rate, measured in Hertz (Hz). For example, a sampling rate of 44,100 Hz (or 44.1 kHz), the standard for CD audio, means that the sound wave's amplitude is measured 44,100 times every second.

Once a sample is taken, its amplitude must be recorded as a number. This is where sampling resolution (also known as bit depth) comes in. The resolution determines how many bits are used to store the value for each sample. This process of assigning a discrete numerical value to each sample's amplitude is called quantisation. A higher bit depth provides a greater number of possible values to represent the amplitude, allowing for a more precise measurement.

For uncompressed audio formats like WAV, the file size can be calculated directly from its properties. It's a product of how often you sample, how much data each sample holds, the duration of the audio, and the number of audio channels.

File Size (bits) = Sampling Rate (Hz) $\times$ Sampling Resolution (bits) $\times$ Time (s) $\times$ Channels

How do we choose an appropriate sampling rate? The answer lies in Nyquist's Theorem. It states that to accurately reconstruct an analogue signal, the sampling rate must be at least twice the highest frequency of the signal. Since the range of human hearing is approximately 20 Hz to 20,000 Hz (20 kHz), the sampling rate for high-fidelity audio must be at least 40,000 Hz. This is why the CD audio standard is 44.1 kHz, providing a small margin above this theoretical minimum.