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

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

Syllabus Unit	Key Topics Covered	Assessment Objectives (AO)
1 Data representation	Binary, hexadecimal, BCD, two’s‑complement, floating‑point, colour depth, sampling rate	AO1, AO2
2 Communication & networks	Bandwidth, latency, OSI model, protocols, data compression, error detection	AO1, AO2, AO3
3 Hardware	CPU, registers, ALU, cache, memory hierarchy, storage devices	AO1, AO2
4 System software	Operating systems, utility software, virtual machines	AO1, AO3
5 Security & ethics	Encryption, authentication, privacy, legal & moral issues	AO2, AO3
6 Databases	Relational model, SQL, normalisation, CRUD operations	AO1, AO2, AO3
7 Algorithms & data structures	Searching, sorting, trees, linked lists, complexity (Big‑O)	AO1, AO2, AO3
8 Programming	Structured programming, OOP concepts, recursion, exception handling	AO1, AO2, AO3
9 Software development	SDLC, testing, documentation, version control	AO2, AO3
10 Multimedia (this unit)	Sampling, colour depth, bitmap vs. vector, video bitrate	AO1, AO2, AO3
11 Emerging technologies (A‑level)	Artificial intelligence, virtualisation, cloud computing	AO2, AO3
12 Problem solving & computational thinking (A‑level)	Algorithm design, abstraction, decomposition, pattern‑recognition	AO1, AO2, AO3

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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.

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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

OSI Layer	Function	Typical Protocols
1 Physical	Transmission media, signalling	Ethernet, Wi‑Fi
2 Data Link	Framing, MAC addressing, error detection	ARP, PPP
3 Network	Routing, logical addressing	IP, ICMP
4 Transport	Segmentation, reliability	TCP, UDP
5‑7 Session‑Presentation‑Application	Session control, data representation, user services	HTTP, FTP, SMTP

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

Structure / Algorithm	Typical Operations	Complexity (Big‑O)
Array	Index access, linear search	O(1) access, O(n) search
Linked list	Insertion/deletion at ends	O(1) insert/delete, O(n) search
Binary search tree	Ordered insert, lookup	O(log n) average, O(n) worst‑case
Sorting (quick‑sort)	Arrange data in order	O(n log n) average, O(n²) worst

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.

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

3.1 Key Terminology (Graphics)

Term	Definition
Pixel	The smallest addressable element of a raster image; a single point of colour.
Resolution	Number of pixels in an image or video frame, expressed as width × height (e.g., 1920 × 1080).
Colour depth / Bit depth	Number of bits used to represent the colour of a single pixel (e.g., 24‑bit = 16.7 million colours).
File header	Metadata at the start of a file that stores information such as resolution, colour depth, and compression type.
Bitmap (raster) image	Image stored as an array of pixels; size grows with resolution and colour depth.
Vector graphic	Image described by mathematical shapes (lines, curves); file size depends mainly on the number of objects, not on resolution.

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

Sampling Rate	Bit Depth	Max Reproducible Frequency	Typical Use	Data Rate (kbps)
8 kHz	8‑bit	4 kHz	Telephone voice	64
44.1 kHz	16‑bit	22.05 kHz	CD audio	1411 (stereo)
96 kHz	24‑bit	48 kHz	High‑resolution audio	3072 (stereo)

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)

Resolution	Pixels / Frame	Colour Depth	Data / Frame (MB)	Bitrate (Mbps) @ 30 fps
640 × 480 (VGA)	307 200	24‑bit	0.88	21.2
1280 × 720 (HD)	921 600	24‑bit	2.64	63.4
1920 × 1080 (Full HD)	2 073 600	24‑bit	5.94	142.6
3840 × 2160 (4K UHD)	8 294 400	24‑bit	23.8	571.2

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?

Task / Content	Best Choice	Reasoning
Photographs, complex scenes	Bitmap (JPEG, PNG)	Colour varies per pixel; raster representation captures real‑world detail.
Logos, icons, line art	Vector (SVG, EPS)	Scales without loss of quality; few geometric objects.
Animated cartoons with solid colours	Vector animation (e.g., Flash) or low‑resolution bitmap	Vector keeps file size small and scales well.
Complex 3‑D renders	Bitmap (rendered frame)	Each pixel stores colour information from lighting calculations.

3.5 Compression – Lossless vs. Lossy

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