Breaking down a signal with Wavelet
Hope the above helps in explaining and interpreting Wavelets. Basically, a Mother Wavelet like the Daubechies wavelet and its Scaling function the Father Wavelet is stretched and shifted along the length of the signal, and the correlation between wavelet and signal recorded as coefficients- the larger the higher the correlation with the signal. Starting from a small wavelet, that caters to the higher frequency (details), the wavelets are stretched into bigger wavelets for approximating the lower frequencies at the higher end of the scale. Actually most wavelet transforms are Discrete and have less scaling and shifting and are yet able to approximate the signal for full re-construction approximate the signal. But in our case we have used a Continuous wavelet transform without redundancy , to go every step of the way and get a full pciture because in highly non-stationary financial data, interesting details are lost if Discrete wavelets are used.
Continuous Wavelet Transform (CWT) of iShares FTSE/Xinhua China 25 Index(966 days till November 20 2010)
Hope the above helps in explaining and interpreting Wavelets. Basically, a Mother Wavelet like the Daubechies wavelet and its Scaling function the Father Wavelet is stretched and shifted along the length of the signal, and the correlation between wavelet and signal recorded as coefficients- the larger the higher the correlation with the signal. Starting from a small wavelet, that caters to the higher frequency (details), the wavelets are stretched into bigger wavelets for approximating the lower frequencies at the higher end of the scale. Actually most wavelet transforms are Discrete and have less scaling and shifting and are yet able to approximate the signal for full re-construction approximate the signal. But in our case we have used a Continuous wavelet transform without redundancy , to go every step of the way and get a full pciture because in highly non-stationary financial data, interesting details are lost if Discrete wavelets are used.
