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.

A signal can also be treated as an observation or the record of an occurrence. Stationarity is a way of describing the characteristics of the signal generating process, which further gives us two categories.

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**Stationary vs Non-Stationary Signals**

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

Speech can be considered to be a form of non-stationary signals. Other synthetic forms of signals are triangular, wave etc. Different approaches have been devised and are used to understand speech signals.

## Comparison Table Between Stationary and Non-Stationary Signals (in Tabular Form)

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

Time | The time period for the stationary signal remains constant at all times. | The time 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 changes constantly during the process. |

Spectral Contents | Spectral content for Stationary signals are constant | Spectral contents are dynamic and keep changing in case of the non-stationary signal. |

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

The characteristic feature of such a signal is that the frequency remains constant throughout.

Stationarity basically 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.

However, stationarity can be maintained in multitone sine waves also, if the frequency remains constant. Both singleton and multitone constant frequency sine waves are hence examples of stationary signals. Both can be represented through two different equations.

It is important to note that even though there are a varied number of frequency components in a multi-tone sinewave. The signal is stationary if the frequency of the said components does not change with time.

Other examples of Stationary Signals are;

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

## What are Non-Stationary Signals?

In simple terms, a non-stationary signal is a signal under a circumstance when the fundamental assumptions that define a stationary signal are no longer valid. This means that a non-stationary signal is the kind of signal where time period, frequency are not constant but variable.

The sine wave representation of a non-stationary equation is hence constantly changing. The spectral contents for such signals are also not constant. Therefore the characteristic feature of non-stationary waves is frequency, that keeps changing constantly between intervals.

Speech signals are natural signals that are non-stationary in nature however they are way more complex and slightly different from non-stationary multitone sinewaves.

Firstly, In the case of speech signals, there may be 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 case of a speech signal, there would be multiple sets of frequency contents, and these contents are likely to change dynamically with respect to time.

Hence the statistical parameters are variable in case of non-stationary signals.

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

- A stationary signal is denoted by a sine-wave equation, which has a constant time period, whereas a non-stationary signal would have a sine wave with a constantly changing time period.
- The frequency for a sine-wave equation remains constant whereas the frequency in the non-stationary signal varies with time.
- The spectral content for a stationary signal in sine wave equation is constant, while in case of a non-stationary equation is ever-changing with respect to time.
- The Fourier transform gives good results for stationary signals while It is not a good representation for non-stationary signals.
- Examples for stationary signals include white noise, single tone sine-wave with constant frequency and multitone sinewave with a constant frequency whereas Non-stationary signal examples include Speech signals and multitone sine wave with varied frequency.

## Conclusion

The system of signals can be categorised in terms of various criteria. Stationarity explains the behaviour of a signal wave in terms of the time period function. The primary difference between a stationary signal and a non-stationary signal can be seen in terms of the sine-wave equation. The stationary signal would have the time period, frequency and spectral content constant, while in the not-stationary signals the all these fundamental assumptions are not valid.

The two categories of signalling systems have been devised by Fourier analysis, however, it has been noticed that the method has it’s own set of limitations and understanding the processing of non-stationary signals require more specific tools.

## References

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

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