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

1.2 Multimedia – Sampling Rate and Resolution

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

1. Sampling Rate (Audio)

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

Key points:

• Higher sampling rates capture more detail, allowing higher frequencies to be reproduced.
• According to the Nyquist theorem, the maximum reproducible frequency is half the sampling rate.
• Increasing the sampling rate increases the amount of data that must be stored or transmitted.

Nyquist Theorem

\$f{\text{max}} = \frac{f{\text{sampling}}}{2}\$

where \$f_{\text{max}}\$ is the highest frequency that can be accurately reproduced.

Impact on File Size

For uncompressed PCM audio, the file size can be estimated by:

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

Typical Sampling Rates

2. Resolution (Video & Images)

Resolution refers to the number of pixels that make up an image or video frame, expressed as width × height (e.g., 1920 × 1080).

• Higher resolution provides more detail and sharper images.
• Each pixel requires colour information; the amount of data per pixel is determined by the colour depth (bits per pixel).
• Increasing resolution raises the amount of data per frame and consequently the overall file size and bandwidth.

Colour Depth

Common colour depths:

• 8‑bit (256 colours)
• 24‑bit (True colour – 16.7 million colours)
• 30‑bit (10 bits per channel – used in HDR video)

Impact on File Size

For an uncompressed video 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}\$

Typical Resolutions and Data Rates

3. Comparative Impact of Changing Parameters

1. Increasing Sampling Rate

   • Improves audio fidelity, especially for high‑frequency content.
   • Raises file size linearly with the sampling rate.
   • Requires more storage and higher bandwidth for streaming.

2. Increasing Resolution

   • Improves visual detail; essential for large displays and close‑up viewing.
   • File size grows quadratically with linear dimension (doubling width and height quadruples pixel count).
   • Higher processing power needed for encoding/decoding and rendering.

3. Balancing Quality and Resources

   • Compression techniques (lossy vs lossless) mitigate the raw data increase.
   • Choosing appropriate sampling rate and resolution depends on target device, network conditions, and content type.

4. Practical Example Calculations

Audio Example: A 3‑minute stereo track recorded at 44.1 kHz with 16‑bit depth.

\$\text{File size} = 44{,}100 \times 16 \times 2 \times 180 = 254{,}016{,}000\ \text{bits} \approx 30.2\ \text{MB}\$

Video Example: A 10‑second clip at 1920 × 1080, 24‑bit colour, 30 fps.

\$\text{Frames} = 30 \times 10 = 300\$

\$\text{File size} = 300 \times 1920 \times 1080 \times 24 = 1{,}492{,}992{,}000\ \text{bits} \approx 177\ \text{MB}\$

5. Summary Checklist

• Higher sampling rate → higher audio bandwidth, larger files.
• Higher resolution → more pixels, larger video files, greater processing demand.
• Always consider the trade‑off between quality and resource constraints.