# Understanding White Noise Autocorrelation

Jan 23, 2024

White noise is a unique signal that plays a critical role in the field of signal processing, engineering, and even day-to-day technology. In this article, we'll understand the concept of autocorrelation and how white noise looks in autocorrelation.

Autocorrelation is a mathematical tool used to identify the similarity between a signal and its delayed version. In other words, it measures the correlation between the signal's current value and the values at different time lags. Autocorrelation is often used for signal detection and identification, noise reduction, and other applications in various fields, such as audio processing, communication systems, and finance.

White noise, in the context of signal processing, is a random signal that has equal intensity at different frequencies. It is characterized by flat power spectral density, a feature that makes it a popular choice for sound masking, testing audio equipment, and even helping people sleep.

So, how does white noise look in autocorrelation? To answer this question, let's examine two main properties of white noise:

Stationarity: White noise is a stationary process, which means its statistical properties do not change over time. This implies that the autocorrelation of white noise would only depend on the time difference between points, not their absolute positions in time.

Independence: White noise is composed of independent, identically distributed random variables. This implies that there is no correlation between the values of the signal at different time instances. In other words, the autocorrelation of white noise should approach zero for all non-zero time lags.

From the properties above, we can conclude that the autocorrelation of white noise would look like an impulse function. In other words, the autocorrelation will have a peak value at zero time lag, indicating perfect correlation, and approach zero for all other time lags, indicating no correlation.

In summary, white noise is characterized by its independence and stationarity properties, and when analyzed in autocorrelation, it appears as an impulse function. This unique behavior allows white noise to serve as an excellent benchmark for testing and analyzing signal processing algorithms and systems.