Data storage and compression：練習問題

Which statement correctly describes the primary difference between lossy and lossless compression?

A mono sound recording is made with a sample rate of \(44,100\) Hz and a sample resolution of \(16\) bits. The recording lasts for \(20\) seconds.

Calculate the uncompressed file size in Kibibytes (KiB), rounded to the nearest whole number.

A 5-minute audio track is recorded using a sample rate of \(44,100 \text{ samples/second}\) and a sample resolution of 16 bits. Assuming the audio is recorded in mono (single channel), calculate the approximate file size in Megabytes (MB). Use the approximation \(1 \text{ MB} = 1,000,000 \text{ bytes}\) for calculation.

A technician needs to calculate the storage requirements for a series of high-resolution images. Which formula correctly calculates the file size of a single image in bits?

Which of the following is a benefit of using lossy compression for a video file being streamed over the internet?

A user needs to reduce the size of a text file containing source code before sending it via email.

State why lossless compression must be used instead of lossy compression for this file.

How many bits are contained within two bytes, and what is the maximum number of distinct values that can be represented by one nibble?

An uncompressed audio track is 3 minutes long, recorded with a sample rate of \(44,100 \) samples per second and a sample resolution of 16 bits (mono). Calculate the uncompressed file size in Mebibytes ( \(MiB \)).

An uncompressed digital image has a resolution of $$800 \times 600$$ pixels and a colour depth of 16 bits.

a) Calculate the uncompressed file size of this image in Kilobytes (KB). Show your working.

b) This image is then compressed using a lossless compression algorithm, reducing its size by 30%. Calculate the compressed file size in Kilobytes (KB).

c) Briefly describe one scenario where lossless compression would be preferred over lossy compression for images, and explain why.

A high-resolution image is captured with a resolution of \(2048 \times 1536\) pixels and a colour depth of 32 bits (True Color with Alpha Channel).

a) Calculate the uncompressed file size of this image in Mebibytes (MiB). Show your working. (Note: Use \(1 \text{ KiB} = 1024 \text{ bytes}\), \(1 \text{ MiB} = 1024 \text{ KiB}\)).

b) Explain the relationship between the colour depth and the visual quality of the image.

c) The user decides to reduce the colour depth from 32 bits to 16 bits to save storage space. State the percentage reduction in file size achieved by this change alone (assuming resolution remains constant).