Signals are measurable quantities in a physical system that are produced within the system. These can be represented in the form of digitally obtained graphs.

The classification of signals can be done under various lenses. It could be done in terms of continuity (Continuous vs discrete), periodicity (Periodic vs Aperiodic), probability (Deterministic versus random), stationarity (stationary versus non-stationary) etc.

## Key Takeaways

- Stationary signals have statistical properties that do not change over time, while non-stationary signals’ properties do change.
- Stationary signals are more predictable and easier to analyze, while non-stationary signals require advanced analysis methods.
- Stationary signals are suitable for linear time-invariant systems, whereas non-stationary signals are more common in real-world applications.

**Stationary vs Non-Stationary Signals**

The difference between stationary and non-stationary signals is that the properties of a static process signal do not change with time. In contrast, a Non-stationary signal is a process inconsistent with time.

Speech can be considered to be a form of non-stationary signal. Other synthetic forms of signs are triangular, wave etc.

## Comparison Table

Parameter of Comparison | Stationary Signals | Non-Stationary |
---|---|---|

Time | The period for the static signal remains constant at all times. | The period for a non-stationary signal varies with time and is not constant. |

Frequency | The frequency of a stationary signal remains constant across the process | The frequency of a Non-stationary wave constantly changes during the process. |

Spectral Contents | Spectral content for Stationary signals is constant | Spectral ranges are dynamic and keep changing in case of non-stationary calls. |

Fourier Equation | Fourier transform is good at representing stationary signals | Fourier transform is non-good at representing non-stationary signals. |

Examples | Single-tone sinewave constant frequency, Multitone sine wave of constant frequency | Speech signals, Multitone sinewave of varied frequency |

## What are Stationary Signals?

A stationary signal is a wave generated by keeping the period and spectral content value constant. A fixed signal can be generated via a software or function generator as a sine wave.

Stationarity explains the behaviour of a signal wave in terms of its frequency and time relation. Here, if the frequency of the sine wave is changed, a completely new wave is devised; hence it will not remain stationary anymore.

Both singleton and multitone constant frequency sine waves are hence examples of stationary signals. Both can be represented through two different equations.

Other examples of Stationary Signals are;

**White Noise**– In the case of white noise, any signal value is equally probable concerning any other signal value at spaced-out reference points.**Temperature**– it can be considered a stationary single for a short time.

## What are Non-Stationary Signals?

A non-stationary signal is when the fundamental assumptions defining a stationary call are no longer valid.

The sine wave representation of a non-stationary equation is hence constantly changing. The spectral contents for such signals are also not constant.

Firstly, speech signals may have multiple frequency components within a given interval of time.

Secondly, the interval itself may be extremely short lesser than 10-30msec as compared to 250msec.

Therefore, in a speech signal, there would be multiple sets of frequency contents, which are likely to change dynamically concerning time.

**Main Differences Between Stationary and Non-Stationary Signals**

- The Fourier transform gives good results for stationary signals, while It is not a good representation for non-stationary signals.
- Examples of stationary signals include white noise, single-tone sine-wave with constant frequency and multitone sinewave with a constant frequency. In contrast, Non-stationary signal examples include Speech signals and multitone sine waves with varied frequencies.

**References**

- https://www.sciencedirect.com/science/article/pii/S0888327004001517
- https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2006.1761

Last Updated : 11 June, 2023

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.

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