Representing images, sound and other data study guide

Build a representation chain

When analysing a real system, first identify whether the original information is analogue or digital. An analogue sensor produces an analogue signal, so an ADC is required before a computer can process its readings as digital data. For output, digital audio can be passed to a DAC to produce an analogue signal. State the direction of conversion rather than simply naming both devices.

Apply bitmap calculations carefully

For a bitmap, identify width, height and colour depth. Calculate the number of pixels first, then multiply by bits per pixel. If the question asks for bytes, divide by 8. If metadata is mentioned, include it only when its size is provided; otherwise state that the calculation is ignoring metadata. Typical metadata includes width, height and colour depth. Distinguish the number of pixels from resolution expressed in dots per inch: an image can be described by its pixel dimensions and also by a dots-per-inch resolution.

Worked reasoning: for an image of width 1024 pixels, height 768 pixels and colour depth 16 bits, the pixel count is 1024 × 768 = 786,432. The storage requirement ignoring metadata is 786,432 × 16 = 12,582,912 bits, which is 1,572,864 bytes. The calculation assumes that the stated colour depth is stored for every pixel.

Compare bitmap and vector approaches

A comparison should link structure to consequence. A bitmap stores a grid of individual pixels, so it can represent pixel-level detail but its storage depends on pixel count and colour depth. A vector graphic stores objects and their properties, making it suitable for geometric images and allowing the image to be described as shapes. In an exam, justify the choice using the nature of the image rather than claiming that one method is always better.

Reason about sound quality and size

For sampled sound, explain separately what sample rate and sample resolution do. A higher sampling rate gives more samples per second and is needed to represent higher frequencies under the Nyquist theorem. A higher sample resolution gives more possible digital values for each sample. Both can increase storage requirements. For a calculation, use sampling rate × duration × sample resolution ÷ 8, and multiply by the number of channels if supplied. Do not confuse sample resolution with sampling rate.

MIDI should be contrasted with sampled sound. MIDI stores event messages describing musical actions, whereas sampled sound stores digital samples of a sound signal. This explains why MIDI can use less storage and why its representation is based on events rather than the complete waveform.

Select compression appropriately

Lossless compression is required when every original value must be recovered. RLE is effective when values occur in consecutive repeated runs; dictionary-based compression uses references to repeated sequences. Lossy compression can produce smaller files by discarding information, but exact recovery is impossible. In an answer, connect the advantage and disadvantage to the need to preserve the original data.

Apply encryption terminology precisely

A message before encryption is plaintext; after encryption it is ciphertext. A cipher is the method used to transform between them, with a key controlling the transformation. For a Caesar cipher, apply the stated shift consistently when encrypting and reverse it when decrypting. Explain that it is easily cracked because the possible shifts are limited. For a Vernam cipher, identify the randomly selected key, explain that the key is used once only, and connect uniform random key selection with perfect security. Contrast this with computationally secure ciphers: they are considered secure because breaking them is impractical, not because they are mathematically impossible to break.

Self-check questions

1. Why is an ADC needed when an analogue sensor is connected to a digital system?
2. What is the difference between colour depth and the number of pixels?
3. Calculate the bitmap storage for a 200 × 100 image with a colour depth of 8 bits, ignoring metadata.
4. Why must the sampling rate be at least twice the highest frequency being recorded?
5. What does an RLE pair represent?
6. Why might MIDI use less storage than sampled audio?
7. What makes a Vernam cipher different from a Caesar cipher and from computationally secure ciphers?

For each answer, include the mechanism and the consequence. Check units in calculations, state assumptions such as ignoring metadata, and distinguish exact reconstruction from approximate reconstruction.