Continuous wavelet transform of frequency breakdown signal. Used symlet
with 5 vanishing moments.
The wavelet transform is a time-frequency representation of a signal. For example, we use it for noise reduction, feature extraction or signal compression.
Wavelet transform of continuous signal is defined as
- is so called mother wavelet,
- denotes wavelet dilation,
- denotes time shift of wavelet and
- symbol denotes complex conjugate.
In case of and , where , and and are integer constants, the wavelet transform is called discrete wavelet transform (of continuous signal).
In case of and , where , the discrete wavelet transform is called dyadic. It is defined as
- is frequency scale,
- is time scale and
- is constant which depends on mother wavelet.
It is possible to rewrite dyadic discrete wavelet transform as
where is impulse characteristic of continuous filter which is identical to for given .
Analogously, dyadic wavelet transform with discrete time (of discrete signal) is defined as