# A Practical Guide to Wavelet Analysis.

@article{Torrence1998APG, title={A Practical Guide to Wavelet Analysis.}, author={Christopher Torrence and Gilbert P. Compo}, journal={Bulletin of the American Meteorological Society}, year={1998}, volume={79}, pages={61-78} }

A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white…

## 11,737 Citations

### Rectification of the Bias in the Wavelet Power Spectrum

- Environmental Science
- 2007

This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different…

### Significance tests for the wavelet cross spectrum and wavelet linear coherence

- Geology
- 2008

This work attempts to develop significance tests for the wavelet cross spectrum and the wavelet linear coherence as a follow-up study on Ge (2007). Conventional approaches that are used by Torrence…

### Significance tests for the wavelet cross spectrum and wavelet linear coherence

- Geology
- 2008

This work attempts to develop significance tests for the wavelet cross spectrum and the wavelet linear coherence as a follow-up study on Ge (2007). Conventional approaches that are used by Torrence…

### Application of the cross wavelet transform and wavelet coherence to geophysical time series

- Computer Science
- 2004

It is demonstrated how phase angle statistics can be used to gain confidence in causal relation- ships and test mechanistic models of physical relationships between the time series and Monte Carlo methods are used to assess the statistical significance against red noise backgrounds.

### Wavelet analysis of covariance with application to atmospheric time series

- Environmental Science
- 2000

Multiscale analysis of univariate time series has appeared in the literature at an ever increasing rate. Here we introduce the multiscale analysis of covariance between two time series using the…

### Some problems on the global wavelet spectrum

- Environmental Science
- 2005

In order to test the validity of the global wavelet spectrum — a new period analysis method based on wavelet analysis, we carried out some simple experiments. In our experiments we used idealized…

### Bayesian modeling and significant features exploration in wavelet power spectra

- Geology
- 2007

This study proposes and justifies a Bayesian ap- proach to modeling wavelet coefficients and finding statis- tically significant features in wavelet power spectra. The approach utilizes ideas…

### Significance and Causality in Continuous Wavelet and Wavelet Coherence Spectra Applied to Hydrological Time Series

- Environmental ScienceHydrology
- 2020

Wavelet transform, wavelet spectra, and coherence are popular tools for studying fluctuations in time series in the form of a bidimensional time and scale representation. We discuss two aspects of…

## References

SHOWING 1-10 OF 34 REFERENCES

### An Introduction to Wavelet Analysis in Oceanography and Meteorology: With Application to the Dispersion of Yanai Waves

- Environmental Science
- 1993

Abstract Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each…

### On estimation of the wavelet variance

- Mathematics
- 1995

SUMMARY The wavelet variance decomposes the variance of a time series into components associated with different scales. We consider two estimators of the wavelet variance: the first based upon the…

### The discrete wavelet transform and the scale analysis of the surface properties of sea ice

- Environmental ScienceIEEE Trans. Geosci. Remote. Sens.
- 1996

The formalism of the one-dimensional discrete wavelet transform (DWT) based on Daubechies wavelet filters is outlined in terms of finite vectors and matrices and the simulated effects of poor instrument resolution on the estimated lead number density and the mean lead width are investigated.

### Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing

- Environmental Science, Geography
- 1995

In this paper, the application of the wavelet transform (WT) to climate time series analyses is introduced. A tutorial description of the basic concept of WT, compared with similar concepts used in…

### Time scales and trends in the central England temperature data (1659–1990): A wavelet analysis

- Environmental Science
- 1997

We have applied the standard wavelet and the adaptive wavelet transform algorithms to the record of the Central England Temperature (CET) from 1659–1990. Peaks in the CET spectra include 7.5±1.0 yr,…

### Wavelet Transforms and their Applications to Turbulence

- Computer Science
- 1992

Wavelet transforms are recent mathematical techniques, based on group theory and square integrable representations, which allows one to unfold a signal, or a field, into both space and scale, and…

### Temporal structure of the southern oscillation as revealed by waveform and wavelet analysis

- Environmental Science
- 1996

Abstract Wavelet transforms (WLT) and waveform transforms (WFT) are effective tools that reveal temporal structure of nonstationary time series. The authors discuss principles and practical aspects…

### Wavelets, Period Doubling, and Time–Frequency Localization with Application to Organization of Convection over the Tropical Western Pacific

- Environmental Science
- 1994

Abstract In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are…

### Orthogonal Wavelet Analysis: Interannual Variability in the Sea Surface Temperature

- Environmental Science
- 1995

Abstract The unique capability of orthogonal wavelets, which have attractive time-frequency localization properties as exemplified by the Meyer wavelet, is demonstrated in a diagnosis of the…

### Improved predictability of two-dimensional turbulent flows using wavelet packet compression

- Environmental Science
- 1992