To accurately reproduce a 2 kHz tone, the sample rate must be greater than twice the highest frequency to be accurately represented. This is based on the Nyquist-Shannon sampling theorem.

Therefore, the minimum sample rate required is 2 * 2 kHz = 4 kHz. However, to avoid aliasing, the sample rate should be significantly higher than the highest frequency of interest. A sample rate of 8 kHz is higher than 4 kHz, so it is sufficient to reproduce a 2 kHz tone accurately. If the sample rate were lower than 4 kHz, aliasing would occur, resulting in a distorted and inaccurate representation of the 2 kHz tone. Aliasing happens when frequencies above the Nyquist frequency (half the sample rate) are incorrectly interpreted as lower frequencies.

Aliasing occurs when a signal's frequency is higher than half the sampling rate. In digital sound reproduction, this leads to the higher frequencies being incorrectly represented as lower frequencies, resulting in a distorted and unpleasant sound.

Aliasing occurs when the sample rate is insufficient to capture the full range of frequencies present in the original sound. Specifically, if a frequency is greater than the Nyquist frequency (which is equal to half the sample rate), it will alias.

Two methods to prevent aliasing are:

• Anti-aliasing filters: These filters are applied to the analog signal before sampling. They attenuate (reduce the amplitude of) frequencies above the Nyquist frequency, preventing them from aliasing. This is a crucial step in any digital audio system.
• Increase the sample rate: Increasing the sample rate raises the Nyquist frequency, allowing for a wider range of frequencies to be accurately represented without aliasing. This is a straightforward way to avoid aliasing, but it requires more storage space and processing power.

A character set is a collection of characters that a computer system can understand and use. It defines the range of characters that can be represented. A character encoding is a method of representing characters as a sequence of bits. It specifies how each character in a character set is translated into a binary code.

Example: UTF-8 is a widely used character encoding. It's a variable-width encoding, meaning it uses different numbers of bytes to represent different characters.

Here's how it works:

• ASCII characters (0-127) are represented using a single byte (8 bits) – the same as ASCII.
• Characters commonly used in Western European languages (e.g., accented characters) are represented using two bytes.
• Characters from other languages (e.g., Chinese, Japanese, Korean) are represented using three or four bytes.

This variable-width approach allows UTF-8 to be backward compatible with ASCII, ensuring that ASCII characters are still represented correctly. It's also efficient for text that primarily uses ASCII characters, as it doesn't waste bytes on those characters. The encoding uses surrogate pairs for characters outside the Basic Multilingual Plane (BMP), which requires four bytes.