← IGCSE Computer Science Paper 1

Lossy compression of a sound by reducing sample rate or sample resolution

Lowering the sample rate or sample resolution of a sound so it needs fewer bits. The file gets smaller, but the lost sound detail can never be recovered.

Part of: IGCSE Computer Science 0478 — 1.3 Data Storage and Compression — Module 38, ACARA Digital Technologies Years 9–10 — Data Compression — Module 31

Understanding Lossy compression of a sound by reducing sample rate or sample resolution in IGCSE Computer Science Paper 1

What it does: The new sample rate (10000 Hz) is used in the size calculation, so the file is half its original size of 19200000 bits. The two sizes are calculated with the old and new resolution, showing that the file is 640000 bits smaller after compression. Work out the size with the original settings and again with the reduced settings. The difference is the saving. Fewer samples per second mean the sound wave is recorded in less detail, so the quality drops.

Common mistakes: Halving the sample rate means dividing by 2. Multiplying by 2 doubles the rate, which gives more data, not less. It should be new_rate = rate // 2. Lossy compression lowers the sample resolution, for example from 16 bits to 8 bits. 24 bits is a higher resolution, so the file would grow. It should be new_res = 8.

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Learning

Duo

A sound is lossy compressed by halving its sample rate. What happens to the file size?

It stays the sameIt gets smaller (about half)

Matches

Sample rate halved, so the original sound can be restored by doubling the rate again

↓

Lossy compression permanently removes sound detail, so doubling the sample rate again cannot bring back the lost data

Applying

Meanings

Term

lossy sound compression

Meaning

Lowering the sample rate or sample resolution of a sound so it needs fewer bits. The file gets smaller, but the lost sound detail can never be recovered.

Practice

rate ← 44100

Testing

Gaps

newrate = rate /

Check Answer

Spots

1rate = 44100

2new_rate = rate * 2

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Quick Questions

1. A sound is lossy compressed by halving its sample rate. What happens to the file size?

A. It gets smaller (about half) ✓

B. It stays the same

Half as many samples are stored each second, so the file needs about half as many bits.

2. Which change is an example of lossy compression of a sound file?

A. Increasing the sample rate from 22,050 Hz to 44,100 Hz

B. Reducing the sample resolution from 16 bits to 8 bits ✓

Fewer bits per sample means less data is kept, so the file shrinks. Increasing the sample rate makes the file bigger.

3. A sound is 4 MiB. After lossy compression by lowering the sample rate, it is 2 MiB. What was the quality loss?

A. Temporary - the detail comes back when it is opened

B. Permanent - the lost detail cannot be recovered ✓

Lossy compression permanently removes data. The original sound cannot be rebuilt from the smaller file.

4. A sound file uses 16-bit sample resolution. It is reduced to 8 bits and nothing else changes. What is the new size compared with the original?

A. Half the original size ✓

B. One quarter of the original size

8 bits is half of 16 bits, so each sample uses half as many bits. The size is halved.

5. To work out the saving after lossy compression of a sound, what should you do?

A. Calculate the size before and after, then compare them ✓

B. Calculate the size once, using the new settings only

Work out the size with the original settings and again with the reduced settings. The difference is the saving.

Match the Pairs

sample rate: 44100 Hz → 22050 Hz → Halving the sample rate takes half as many samples each second, so the file size is halved and some sound detail is lost

sample resolution: 16 bits → 8 bits → Each sample is stored with half as many bits, so the file size is halved but the sound is less accurate

To find the size after halving the sample rate, recalculate with the new rate: rate × resolution × seconds → 20000 / 2 × 16 × 60 = 10000 × 16 × 60 = 9600000 bits

To show the saving from reducing 16 bits to 8 bits, compare the size before and after → before: 8000 × 16 × 10 = 1280000 bits, after: 8000 × 8 × 10 = 640000 bits

Sample rate halved, so the original sound can be restored by doubling the rate again → Lossy compression permanently removes sound detail, so doubling the sample rate again cannot bring back the lost data

Reducing 16 bits to 8 bits makes the sound file bigger because the sound is simpler → Fewer bits per sample means fewer total bits, so the file gets smaller, not bigger

Key Term

lossy sound compression

Lowering the sample rate or sample resolution of a sound so it needs fewer bits. The file gets smaller, but the lost sound detail can never be recovered.

Fill in the Blanks

1. rate = 44100 newrate = rate / 2

Hint: Type the number you divide the sample rate by to halve it.

2. bits = 16 newbits = bits / 2

Hint: Type the arithmetic operator that cuts the 16-bit sample resolution down to 8 bits.

3. rate = 44100 seconds = 10 sizebefore = rate * 16 * seconds

Hint: Type the variable for the length of the sound, which is multiplied in to find the size before compression.

4. sizeafter = newrate * 8 * seconds saving = sizebefore - sizeafter

Hint: Type the operator that works out how much smaller the file is after compression.

5. detaillost = True canrestore = False

Hint: Type the Boolean value that shows the removed sound detail cannot be recovered after lossy compression.

Spot the Error

Question 1

A rate = 44100

B new_rate = rate * 2

C res = 16

D bits = new_rate * res * 10

Line B — Halving the sample rate means dividing by 2. Multiplying by 2 doubles the rate, which gives more data, not less. It should be new_rate = rate // 2.

Question 2

A rate = 8000

B res = 16

C new_res = 24

D new_bits = rate * new_res * 5

Line C — Lossy compression lowers the sample resolution, for example from 16 bits to 8 bits. 24 bits is a higher resolution, so the file would grow. It should be new_res = 8.

Question 3

A rate = 20000

B res = 8

C bits = rate + res * 30

D bytes = bits / 8

Line C — File size in bits is sample rate x sample resolution x length in seconds. The rate and resolution must be multiplied, not added. It should be bits = rate * res * 30.

Question 4

A old_bits == 44100 * 16 * 10

B new_bits = 22050 * 16 * 10

C saved = old_bits - new_bits

Line A — == compares two values, so nothing is stored in old_bits. Assigning the size before compression needs a single =. It should be old_bits = 44100 * 16 * 10.

Question 5

A old = 44100 * 16 * 10

B new = 22050 * 16 * 10

C saved = old - new

D saved_bytes = saved * 8

Line D — The saving is in bits. To change bits into bytes you divide by 8, not multiply. It should be saved_bytes = saved / 8.

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