For input S₁ and output S₂, the characteristics of µ-law companding is correctly expressed as : 

Concept:

In µ-law companding, the amplitude of the input signal is compressed using a logarithmic function to improve dynamic range in digital communication systems.

This technique is commonly used in North America and Japan for compressing audio signals in telephony.

Expression:

The standard formula for µ-law companding (ignoring sign for magnitude) is:

\( |S_2| = \frac{\ln(1 + \mu \cdot |S_1|)}{\ln(1 + \mu)} \)

Explanation:

Where,

• |S₁| is the magnitude of the input signal
• |S₂| is the compressed output
• µ is the compression parameter (typically 255)

This expression ensures that lower amplitude signals are encoded with higher resolution, enhancing low-level signal quality while maintaining a manageable dynamic range for the overall signal.

Correct Option:

 The correct expression that matches this is:  4) |S2| = ln(1 + µ|S1|) / ln(1 + µ)