Show understanding of the impact of changing the sampling rate and resolution

1.2 Multimedia – Sampling Rate, Resolution & Image Types

Learning Objective

Show understanding of the impact of changing the sampling rate and resolution on:

• Perceived quality of audio and video
• File size and storage requirements
• Transmission bandwidth and processing load
• Choice between bitmap and vector graphics for a given task

0. Cambridge Computer Science (9618) – Syllabus Overview & AO Alignment

1. Key Concepts for the Whole Syllabus

• Computational thinking – decomposition, pattern‑recognition, abstraction, algorithmic design.
• Data representation – binary, hexadecimal, BCD, two’s‑complement, floating‑point, colour models, audio/video sampling.
• Communication – bandwidth, latency, protocols, OSI model, error detection/correction.
• Hardware fundamentals – CPU, registers, ALU, cache, main memory, secondary storage.
• System software – operating systems, virtual machines, utilities.
• Security & ethics – encryption, authentication, privacy, legal frameworks.
• Databases – relational model, SQL, normalisation.
• Algorithms & data structures – searching, sorting, linked lists, trees, complexity.
• Programming paradigms – structured, object‑oriented, recursion, exception handling.
• Software development lifecycle – planning, design, implementation, testing, maintenance.

2. Core AS Topics (Units 1‑12) – Concise Reference

2.1 Data Representation

• Binary ↔ Decimal: 101101₂ = 1·2⁵ + 0·2⁴ + 1·2³ + 1·2² + 0·2¹ + 1·2⁰ = 45₁₀
• Hexadecimal: Group binary in fours. 1011 0110₂ = B6₁₆.
• BCD (Binary‑Coded Decimal): Each decimal digit stored as 4‑bit binary (e.g., 27 → 0010 0111).
• Two’s‑complement (8‑bit) example: –23 → 23₁₀ = 0001 0111₂ → invert → 1110 1000 → add 1 → 1110 1001₂.
• Overflow illustration: 200₁₀ + 100₁₀ = 300₁₀ → 100101100₂ (9 bits). In an 8‑bit unsigned register it wraps to 00101100₂ = 44₁₀ (overflow).
• Floating‑point (IEEE 754 single precision): 1 bit sign, 8 bit exponent (bias 127), 23 bit mantissa.

2.2 Communication & Networks

Bandwidth vs. latency: Bandwidth is the maximum data rate (bits s⁻¹); latency is the time for a single bit to travel from source to destination. High‑definition video needs both high bandwidth and low latency for smooth streaming.

2.3 Hardware

• CPU cycle: Fetch → Decode → Execute → Write‑back.
• Registers: General‑purpose, program counter, status register.
• Cache hierarchy: L1 (fastest, smallest) → L2 → L3; reduces average memory access time.
• Memory addressing: Byte‑addressable; 32‑bit address space → 4 GB maximum.
• Secondary storage: HDD (magnetic), SSD (flash), optical (CD/DVD), each with characteristic access time and capacity.

2.4 System Software

• Operating system – manages processes, memory, I/O, file systems; provides API to applications.
• Virtual machines – abstract hardware (e.g., Java Virtual Machine) enabling platform independence.
• Utility software – backup, antivirus, compression tools.

2.5 Security & Ethics

• Symmetric encryption – same key for encrypt/decrypt (e.g., AES).
• Asymmetric encryption – public/private key pair (e.g., RSA).
• Authentication – passwords, biometrics, two‑factor.
• Legal/ethical issues – copyright, data protection (GDPR), cyber‑bullying.

2.6 Databases

• Relational model – tables (relations), primary keys, foreign keys.
• SQL basics: SELECT … FROM … WHERE …, INSERT, UPDATE, DELETE.
• Normalisation – eliminate redundancy (1NF, 2NF, 3NF).

2.7 Algorithms & Data Structures

2.8 Programming (Structured & OOP)

• Control structures – sequence, selection (if/else, switch), iteration (for, while).
• Procedures / functions – modularise code, pass parameters, return values.
• Object‑oriented concepts – classes, objects, inheritance, encapsulation, polymorphism.
• Recursion – a function calling itself; base case prevents infinite loop.
• Exception handling – try / catch / finally blocks to manage runtime errors.

2.9 Software Development

• SDLC phases: requirements → design → implementation → testing → deployment → maintenance.
• Testing types: unit, integration, system, acceptance.
• Documentation: user manuals, API docs, version‑control history (Git).

2.10 Emerging Technologies (A‑Level Extension)

• Artificial Intelligence – machine learning basics, neural networks.
• Virtualisation – hypervisors, containers.
• Cloud computing – SaaS, PaaS, IaaS models.
• Internet of Things – sensors, edge computing.

3. Multimedia – Sampling Rate, Resolution & Image Types (Core Focus)

3.1 Key Terminology (Graphics)

3.2 Audio – Sampling Rate & Bit Depth

3.2.1 What is Sampling?

The sampling rate is the number of samples taken each second from a continuous analogue signal. It is measured in hertz (Hz) or kilohertz (kHz).

Nyquist theorem – the highest frequency that can be reproduced without aliasing is half the sampling rate:

\(f{\text{max}} = \dfrac{f{\text{sampling}}}{2}\)

3.2.2 Bit Depth (Audio Resolution)

Bit depth determines the number of discrete amplitude levels that can be stored for each sample. More bits give a larger dynamic range and lower quantisation noise.

• 8‑bit ≈ 48 dB dynamic range (telephone quality)
• 16‑bit ≈ 96 dB (CD quality)
• 24‑bit ≈ 144 dB (professional recording)

3.2.3 Impact on File Size (Uncompressed PCM)

\[

\text{File size (bits)} = f_{\text{sampling}} \times \text{bit depth} \times \text{channels} \times \text{duration (s)}

\]

3.2.4 Typical Audio Formats

3.2.5 Example Calculation (Audio)

Three‑minute stereo track, 44.1 kHz, 16‑bit:

\[

\begin{aligned}

\text{File size} &= 44{,}100 \times 16 \times 2 \times 180\\

&= 254{,}016{,}000\ \text{bits}\\

&\approx 30.2\ \text{MB}

\end{aligned}

\]

3.3 Video & Images – Resolution, Colour Depth & File Size

3.3.1 Resolution

Resolution = width × height (pixels). Doubling both dimensions quadruples the pixel count, so file size grows quadratically.

3.3.2 Colour Depth (Bits per Pixel)

• 8‑bit = 256 colours (e.g., GIF, simple graphics)
• 24‑bit = True colour (16.7 million colours)
• 30‑bit = 10 bits per channel, used for HDR video

3.3.3 Impact on Uncompressed File Size

For a single frame:

\[

\text{Frame size (bits)} = \text{width} \times \text{height} \times \text{colour depth}

\]

For a video clip of n frames:

\[

\text{Video size (bits)} = n \times \text{width} \times \text{height} \times \text{colour depth}

\]

3.3.4 Typical Resolutions & Approximate Uncompressed Bitrates (30 fps)

3.3.5 Example Calculation (Video)

10‑second clip, 1920 × 1080, 24‑bit colour, 30 fps:

\[

\begin{aligned}

\text{Frames} &= 30 \times 10 = 300\\[4pt]

\text{File size} &= 300 \times 1920 \times 1080 \times 24\\

&= 1{,}492{,}992{,}000\ \text{bits}\\

&\approx 177\ \text{MB}

\end{aligned}

\]

3.4 Bitmap vs. Vector Graphics

3.4.1 Definitions

• Bitmap (raster) image – stored as a grid of pixels; size depends on resolution and colour depth.
• Vector graphic – stored as a set of geometric primitives (lines, curves, shapes); size depends mainly on the number of objects, not on pixel dimensions.

3.4.2 File‑size Estimation (Bitmap)

\[

\text{File size (bytes)} = \frac{\text{width} \times \text{height} \times \text{colour depth}}{8}

\]

Example: 800 × 600 pixel image, 24‑bit colour → \(\frac{800 \times 600 \times 24}{8}=1{,}440{,}000\) bytes ≈ 1.37 MB.

3.4.3 When to Use Which?

3.5 Compression – Lossless vs. Lossy

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