Show understanding of how sound is represented and encoded

1.2 Multimedia – Sound Representation & Encoding

🎧 1.2.1 What is Sound?

Sound is a vibration that travels through a medium (air, water, solids). Think of it like a ripple in a pond – the ripples move outward, carrying energy. When these ripples reach our ears, they are interpreted as music, speech, or noise.

📊 1.2.2 From Waves to Numbers

To store sound on a computer, we need to turn the continuous wave into a sequence of numbers. This process involves two key steps:

1. Sampling – taking a snapshot of the wave at regular time intervals.
2. Quantisation – assigning each snapshot a finite number of bits.

⏱️ 1.2.3 Sampling

Sampling rate, denoted $f_s$, is how many times per second we measure the wave. The time between samples is $T_s = \frac{1}{f_s}$.

The Nyquist theorem tells us we must sample at least twice the highest frequency we want to capture: $$ f_s \ge 2 f_{\text{max}} $$ For human hearing (up to 20 kHz), a common choice is $f_s = 44.1$ kHz (CD quality).

🔢 1.2.4 Quantisation

Each sample is rounded to the nearest value that can be represented with $N$ bits. The number of possible levels is $2^N$. For example, 16‑bit audio gives $65\,536$ levels.

The quantisation step size (resolution) is: $$ \Delta = \frac{V_{\text{max}} - V_{\text{min}}}{2^N} $$ where $V_{\text{max}}$ and $V_{\text{min}}$ are the maximum and minimum voltage the ADC can read.

💾 1.2.5 Encoding Formats

📈 1.2.6 Compression & Lossless vs Lossy

Compression reduces file size by removing redundant or inaudible information.

• Lossless (e.g., FLAC): no data is lost; perfect reconstruction.
• Lossy (e.g., MP3, AAC): some data is discarded; smaller size but slight quality loss.

🗂️ 1.2.7 Example: PCM Sample Table

🎓 1.2.8 Key Takeaways

• Sound is a continuous wave that must be sampled and quantised to be stored digitally.
• The sampling rate determines how accurately we capture high‑frequency content.
• More bits per sample mean finer amplitude resolution.
• Encoding formats balance file size against audio quality.
• Compression can be lossless (perfect fidelity) or lossy (small size, slight loss).