1.2 Multimedia 多媒体表示

Syllabus learning goals 考纲学习目标

第一次学习本章？ 先阅读完整的 Chapter 1.2 Multimedia 课本教材。教材从零解释概念，并在每个阶段安排 Past Paper 原题；本页继续作为考前复习与 Mark Scheme wording 总结。

完成本节后，学生需要能够：

• 解释 bitmapped image 如何编码，并正确使用 pixel、file header、image resolution、screen resolution 和 colour depth/bit depth。
• 估算 bitmap image 的 file size。
• 解释 image resolution 和 colour depth 改变时，对 image quality 与 file size 的影响。
• 解释 vector graphic 如何使用 drawing object、property 和 drawing list 编码。
• 根据任务特点选择 bitmap 或 vector graphic，并给出理由。
• 解释 analogue sound 如何通过 sampling、sampling rate 和 sampling resolution 编码为 digital data。
• 解释 sampling rate 与 sampling resolution 改变时，对 accuracy 和 file size 的影响。

简答题不要只写 “quality improves” 或 “file gets bigger”。必须说明哪个参数改变、数据量为什么改变，以及图像或声音为什么更接近原始数据。

1 Bitmap images 位图图像

Bitmap image 是由规则网格中的 pixels 构成的。每个 pixel 只有一种 colour，该颜色由一个 unique binary code 表示。各 pixel 的 colour codes 按固定顺序存储，file header 则保存解释这些数据所需的 metadata。

Core terms

Describe how a bitmap is encoded [3]

• The image is made of pixels, and each pixel has one colour.
• Each colour has a unique binary code.
• The code for the colour of each pixel is stored in sequence.

这三个 bullet points 分别说明组成单位、编码方法和存储顺序。只写 “the image is stored in binary” 通常不足以得分。

Colour depth and number of colours

若 colour depth 为 n bits，每个 pixel 最多可选择 2^n 种颜色：

1 bit  -> 2 colours
4 bits -> 16 colours
8 bits -> 256 colours
16 bits -> 65 536 colours

2 Bitmap file-size calculations 位图文件大小

未压缩 bitmap 的估算公式：

File size in bits
= width in pixels x height in pixels x colour depth in bits

若 colour depth 已用 bytes 表示，就不应再次除以 8。

Worked example

一张图像宽 1000 pixels、高 2000 pixels、colour depth 为 16 bits：

Number of pixels = 1000 x 2000 = 2 000 000
File size in bits = 2 000 000 x 16 = 32 000 000 bits
File size in bytes = 32 000 000 / 8 = 4 000 000 bytes
File size in MB = 4 000 000 / 1 000 000 = 4 MB

Unit conversion

考试必须先判断题目使用 decimal prefix 还是 binary prefix。MB 与 MiB 的除数不同。

Why the actual file may be larger

计算公式通常只估算 pixel data。实际文件还可能包含：

• A file header.
• Metadata about the image.

因此实际 file size 可能比估算值大。

3 Effects of changing bitmap parameters 参数变化

Increasing image resolution

• More pixels are stored/available.
• More detail can be represented, so the image is sharper / less pixelated / closer to the original。
• More pixel codes must be stored, so file size increases。

Decreasing image resolution

• Fewer pixels are stored。
• Detail is lost, so the image becomes less sharp or more pixelated。
• Less data is stored, so file size decreases。

Increasing colour depth

• More bits are used per pixel.
• A greater range of colours/shades can be represented。
• Colours may be closer to the original and the image may appear more realistic。
• More data is stored, so file size increases。

Decreasing colour depth

• Fewer bits are used per pixel and fewer colours are available。
• Colour accuracy/detail decreases, so the image may not match the original as closely。
• Less data is stored, so file size decreases。

Mark-secure causal chain

Increasing the image resolution means more pixels are stored. This allows more detail, so the image is sharper and less pixelated. More pixel data must be stored, so the file size increases.

题目若分别给 Image quality 与 File size 两个栏，应在对应栏中分别回答，不要把两个结果混在同一句模糊描述中。

4 Vector graphics 矢量图形

Vector graphic 不逐个存储 pixels，而是保存组成图形的 objects 以及重新绘制它们所需的数据。

Describe a drawing list [2]

• It contains a list of the objects/shapes in the drawing.
• It stores the commands, descriptions or mathematical equations required to draw each object, including its properties。

5 Choosing bitmap or vector 选择图像类型

选择必须联系题目场景，而不是背诵“vector 一定更好”。

Bitmap is suitable when

• 图像是 photograph，包含连续色调、阴影和大量细节。
• 需要逐个 pixel 编辑。
• 图像不会频繁放大到远高于原始 resolution。

缺点是放大后可能 pixelated，且高 resolution 与高 colour depth 会产生较大文件。

Vector is suitable when

• 图像由 simple geometric shapes 构成，例如 logo、icon、diagram 或文字。
• 图像需要反复缩放；对象可重新计算和绘制，因此 can be resized without becoming pixelated / without loss of quality。
• 需要方便地修改单个 object 或 property。
• 简单图形通常只需保存 drawing objects 与 properties，文件可能较小。

Justification pattern

A vector graphic is suitable for the logo because it is made from simple shapes and may need to be resized. The objects are redrawn from their stored properties, so it can be enlarged without becoming pixelated.

6 Representing sound 声音表示

真实声音波形是 analogue data：数值 changes continuously，在一定范围内可以取任意值。计算机需要把连续波形转换成一系列离散的 digital values。

Core terms

Explain analogue-to-digital conversion

• The amplitude of the analogue sound wave is measured at regular intervals.
• Each sampled amplitude is assigned a corresponding binary value.
• The binary values are stored in sequence.

对于 2-mark 题，前两点通常已足够；对于 3-mark describe 题，要补充存储顺序。

7 Sampling rate and resolution 参数影响

Increasing sampling rate

• More samples are taken per second; time gaps between samples become smaller。
• The digital waveform more closely resembles the analogue waveform, so accuracy improves。
• More samples must be stored, so file size increases。

Increasing sampling resolution

• More bits are used per sample.
• More amplitude values can be represented，so each stored value can be closer to the original amplitude。
• Quantisation error is reduced and accuracy improves。
• More bits are stored for every sample, so file size increases。

Decreasing either setting reverses these effects. Changing duration changes file size, but does not by itself change sampling accuracy。

Sound file-size formula

对于单声道、未压缩声音：

File size in bits
= sampling rate x sampling resolution x duration in seconds

若有多个 channels，再乘以 channel 数量。

例：50 kHz、16-bit、20 minutes：

50 000 x 16 x (20 x 60)
= 960 000 000 bits
= 120 000 000 bytes
= 120 MB

Performance in a real system

更高 sampling rate 不只影响声音本身，还可能导致：

• More data to transmit, so transmission takes longer or requires more bandwidth。
• Storage fills faster, so fewer recordings can be retained。

8 Command words and common mistakes 答题方法

常见失分：

• 把 image resolution 与 screen resolution 混为一谈。
• 把 colour depth 写成 image 中 pixel 的总数。
• 忘记从 bits 除以 8 转换为 bytes。
• MB 题使用 1024，或 MiB 题使用 1000。
• 只写 “better quality”，没有说明 more pixels、more samples 或 more amplitude values。
• 认为增加 recording duration 会提高声音 accuracy。

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本材料依据 9618 syllabus 1.2 的七项要求，并综合本页所列 2021-2025 past-paper questions 及 mark schemes。简答模板优先采用可独立评分的 cause-and-effect wording。