Stationary vs Non-stationary

July 26, 2024

In signal processing, the concepts of stationary and non-stationary are used to describe the properties of a signal over time.

Stationary Signal #

A signal is called stationary if its statistical properties do not change over time. These statistical properties include mean, variance, and correlation functions. There are two types of stationarity:

1. Weak Stationarity (or Wide-Sense Stationarity): The signal has a constant mean and variance over time, and the correlation function depends only on the time difference between two points, not on the specific time points themselves.

2. Strong Stationarity (or Strict-Sense Stationarity): All probability distributions of the signal do not change over time.

Non-Stationary Signal #

A signal is called non-stationary if its statistical properties change over time. This means the mean, variance, or correlation functions of the signal change over time. Non-stationary signals often appear in systems where characteristics change over time, such as audio signals, medical signals (heart rate, brain waves), and many other real-world data.

Applications and Processing #

1. Processing Stationary Signals: Methods like Fourier Transform (FT) and Fast Fourier Transform (FFT) are commonly applied because they assume the signal is stationary.

2. Processing Non-Stationary Signals: Time-frequency analysis methods such as Short-Time Fourier Transform (STFT), Wavelet Transform, and Empirical Mode Decomposition (EMD) are often used to analyze and process non-stationary signals.

Understanding the difference between stationary and non-stationary signals is crucial in choosing the appropriate signal processing methods to achieve accurate and efficient results.