Standard Article

Time–Frequency Analysis

Signal Processing

  1. Rosario Ceravolo

Published Online: 15 SEP 2009

DOI: 10.1002/9780470061626.shm047

Encyclopedia of Structural Health Monitoring

Encyclopedia of Structural Health Monitoring

How to Cite

Ceravolo, R. 2009. Time–Frequency Analysis. Encyclopedia of Structural Health Monitoring. .

Author Information

  1. Politecnico di Torino, Dipartimento di Ingegneria Strutturale e Geotecnica, Torino, Italy

Publication History

  1. Published Online: 15 SEP 2009


Time–frequency analysis has been recently introduced into many research fields, ranging from seismic signal processing to biomedical engineering. Interest in this representation is motivated by the limitations of classical spectral estimation techniques in analyzing strongly nonstationary behaviors.

Owing to the importance of nonstationary components in vibration signals, several studies have proposed the adoption of time–frequency analysis in structural identification and damage assessment. Many authors have applied linear tools, such as the short-time Fourier transform and the wavelet transform, or in some cases, their squared magnitudes, known as spectrogram and scalogram, respectively.

The adoption of a quadratic representation makes it possible to overcome limitations due to the time–frequency resolution, since energetic and correlative transforms are not based on signal segmentation. Specifically, among the quadratic transforms, those belonging to the Cohen class are characterized by their invariance to time and frequency shifts. This property allows for a correct physical interpretation of the mechanical response, thus justifying the interest that many researchers have shown for this approach.

The present article is intended as a comprehensive overview of some recent advances in the field of time–frequency analysis for structural identification. We focus on the shift-invariant class, including the spectrogram. Other time–frequency analysis techniques include, but are not limited to, wavelet analysis (see Wavelet Analysis) and empirical mode decomposition combined with Hilbert transform (see Damage Detection Using the Hilbert–Huang Transform).


  • time–frequency analysis;
  • time-varying spectra;
  • structural identification;
  • flexible structures;
  • modal testing