Quantization Error:
Quantization is the process of converting a continuous signal into a discrete signal by dividing the continuous signal into a finite number of levels. The quantization process introduces an error known as quantization error.

Definition:
The difference between the unquantized signal x(n) and the quantized signal xq(n) is known as the quantization error.

Explanation:
Quantization is necessary when representing a continuous signal with a finite number of bits. In this process, the continuous signal is divided into smaller intervals known as quantization levels. The value of the continuous signal is approximated to the nearest quantization level.

The quantization error occurs due to the inability to represent the continuous signal exactly with the available quantization levels. As a result, there is always a difference between the original unquantized signal and the quantized signal.

Significance:
The quantization error is an important parameter in quantization as it determines the accuracy of the quantized signal. A smaller quantization error indicates a more accurate representation of the original signal.

Characteristics:
The quantization error has the following characteristics:

1. Randomness: The quantization error is random and cannot be predicted or controlled. It depends on the input signal and the quantization process.

2. Amplitude: The amplitude of the quantization error depends on the number of quantization levels. A larger number of quantization levels result in a smaller quantization error.

3. Distribution: The quantization error follows a uniform distribution, assuming the input signal is uniformly distributed.

4. Mean Square Error: The mean square error (MSE) is a measure of the average squared difference between the unquantized signal and the quantized signal. It is commonly used to evaluate the performance of quantization.

5. Bit Depth: The bit depth, which represents the number of quantization levels, directly affects the quantization error. Increasing the bit depth reduces the quantization error and improves the accuracy of the quantized signal.

Conclusion:
The quantization error is the difference between the unquantized signal and the quantized signal. It is a random error that cannot be eliminated completely. Understanding and minimizing the quantization error is essential in digital signal processing to ensure accurate signal representation.