wavelet
Sign in to saveA wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. thumb|Seismic wavelet
Article
29 sectionsContents
- Etymology
- Wavelet theory
- Continuous wavelet transforms (continuous shift and scale parameters)
- Discrete wavelet transforms (discrete shift and scale parameters, continuous in time)
- Multiresolution based discrete wavelet transforms (continuous in time)
- Time-causal wavelets
- Mother wavelet
- Comparisons with Fourier transform (continuous-time)
- Definition of a wavelet
- Scaling filter
- Scaling function
- Wavelet function
- History
- Timeline
- Wavelet transforms
- Generalized transforms
- Applications
- As a representation of a signal
- Wavelet denoising
- Multiscale climate network
- List of wavelets
- Discrete wavelets
- Continuous wavelets
- Real-valued
- Complex-valued
- See also
- References
- Further reading
- External links
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. thumb|Seismic wavelet
For example, a wavelet could be created to have a frequency of middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications.