3.6 · Multimedia Digitisation

Goal: explain briefly how images, audio and video are digitised, and reason about file size trade-offs.

How images are digitised

Step 1 · Sampling — divide into pixels

An image is broken into a grid of pixels (picture elements). The more pixels per inch, the higher the resolution.

Original picture  →  640 × 480 grid  →  307,200 pixels
                                       ▢ ▢ ▢ ▢ ▢ ▢ ▢ …
                                       ▢ ▢ ▢ ▢ ▢ ▢ ▢ …
                                       …

Step 2 · Quantisation — encode each pixel's colour

Each pixel is stored as a colour code. Two common schemes:

Scheme	Bits per pixel	Colours
1-bit black & white	1	2
8-bit greyscale	8	256
24-bit RGB true colour	24 (8 per channel)	16,777,216
32-bit ARGB	32 (8 alpha + 8 R + 8 G + 8 B)	16M with transparency

The bit depth (or colour depth) determines the number of representable colours: 2ⁿ for n bits.

Image file size estimate

file size ≈ width × height × bit depth ÷ 8   (in bytes, uncompressed)

A 1920×1080 24-bit photo:

1920 × 1080 × 24 ÷ 8 = 6,220,800 bytes ≈ 5.9 MB (uncompressed BMP)

Compression (JPG, PNG) typically reduces this by 5×–20×.

Worked example · Why JPG is smaller than BMP for photos

JPG uses lossy compression that discards detail the eye is unlikely to notice (high-frequency components in colour channels). The same 5.9 MB BMP often becomes a 600 KB JPG with imperceptible quality loss.

How audio is digitised

Sound is a continuous pressure wave. To digitise it:

Step 1 · Sampling rate — how often to measure

The microphone is sampled at regular intervals. Common rates:

Sampling rate	Use case
8 kHz	Telephone
22.05 kHz	Low-quality voice recording
44.1 kHz	CD audio
48 kHz	Pro audio, video
96 / 192 kHz	High-resolution audio

Higher rates capture higher frequencies (Nyquist theorem: ≥ 2× the highest frequency to be preserved).

Step 2 · Bit depth — how precise each sample is

Bit depth	Use case
8-bit	Telephone, simple toys
16-bit	CD audio, MP3
24-bit	Studio recording

Step 3 · Channels

Channels	Description
Mono	1 channel
Stereo	2 channels (L + R)
5.1 surround	6 channels

Audio file size estimate

file size ≈ sample rate × bit depth × channels × duration ÷ 8   (in bytes, uncompressed)

3 minutes of CD-quality stereo audio:

44,100 × 16 × 2 × 180 ÷ 8 = 31,752,000 bytes ≈ 30 MB

MP3 compression brings this to about 3 MB.

How video is digitised

Video is a sequence of still frames (each digitised as an image) plus an audio track.

Property	Examples
Frame rate (fps)	24 (film), 30 (TV), 60 (high motion), 120 (slow-mo)
Resolution	720p (1280×720), 1080p, 4K (3840×2160), 8K
Bit depth	typically 8 bits per channel (24 bpp)
Codec	H.264, H.265, AV1, VP9

Video file size estimate (uncompressed)

file size ≈ width × height × bit depth × frame rate × duration ÷ 8

For 1080p 30fps 24-bit, 1 minute:

1920 × 1080 × 24 × 30 × 60 ÷ 8 ≈ 11 GB

Real H.264 compressed video for the same minute → about 70–200 MB (50–150× smaller).

Compression — lossless vs lossy

Type	What it does	Pros	Cons	Examples
Lossless	Encodes the exact original; perfectly reversible	No quality loss	Smaller savings	PNG, FLAC, ZIP
Lossy	Discards data the human senses miss	Much smaller files	Cannot recover original	JPG, MP3, MP4

When to use which

• Photographs / music for casual listening → lossy is fine.
• Medical imaging / archive masters → lossless.
• Diagrams, icons, screenshots → lossless (PNG) because hard edges suffer in JPG.

Sampling theorem (simplified)

To reproduce a signal containing frequencies up to F, you need to sample at at least 2 × F times per second (Nyquist rate).

Audio CDs sample at 44.1 kHz because the human ear hears up to ~20 kHz, and 2 × 20 = 40 plus a safety margin → 44.1 kHz.

Common student mistakes

• Confusing sampling rate with bit rate (bit rate combines both with channel count).
• Saying "lossless compression makes the file smaller without changing it" — it changes the encoding, not the content.
• Treating GIF as a video format — GIF is an animated image format; modern web uses MP4 or WebM.

Practice activity

Estimate the size of:

1. A 12-megapixel photo at 24-bit colour, uncompressed.
2. A 5-minute mono voice memo at 16-bit, 8 kHz.
3. A 30-second 720p video at 30 fps, uncompressed.

Calculation hints

1. 12,000,000 × 24 ÷ 8 ≈ 36 MB
2. 8000 × 16 × 1 × 300 ÷ 8 ≈ 4.8 MB
3. 1280 × 720 × 24 × 30 × 30 ÷ 8 ≈ 2.5 GB

Exam-style question

Q (4 marks): Explain how an audio CD with 16-bit, 44.1 kHz, stereo sampling stores 60 seconds of music. Calculate the storage required (ignore overheads).

Sample answer:

The microphone signal is sampled 44,100 times per second on each of the two channels (stereo). Each sample is stored as a 16-bit integer representing the signal level at that instant. The 60-second stream contains 44,100 × 2 × 60 = 5,292,000 samples. Each sample is 2 bytes (16 bits), so the total storage is 5,292,000 × 2 = 10,584,000 bytes ≈ 10.1 MB.

Key takeaways

• Image = pixel grid + colour depth.
• Audio = sample rate × bit depth × channels.
• Video = frames + audio + compression.
• Lossy compression trades quality for size; lossless preserves all detail.

➡️ Next: 3.7 File Formats