White noise is considered stationary in a statistical sense. This means that its statistical properties, such as its mean and variance, remain constant over time.
Here's why:
- Constant Mean: The average value of white noise is always zero. This means that the signal doesn't have any trend or drift over time.
- Constant Variance: The variability of white noise is the same at all points in time. This means that the signal doesn't become more or less noisy over time.
- Zero Autocorrelation: White noise has no correlation between its values at different points in time. This means that knowing the value of the signal at one point in time doesn't give you any information about its value at any other point in time.
These properties make white noise a useful tool in various applications, such as:
- Audio Engineering: White noise can be used to mask unwanted sounds or create a sense of space.
- Signal Processing: White noise can be used to test the performance of filters or other signal processing systems.
- Random Number Generation: White noise can be used to generate random numbers.
While white noise is theoretically stationary, real-world signals often have some degree of non-stationarity. This is because real-world signals are often affected by factors that can change over time, such as environmental noise or changes in the system being measured.
However, for many practical purposes, white noise can be treated as stationary.
