Table 1.

Mother wavelet coefficients.

Wavelet	L: co- efficient number	High-pass filter (G) coefficients	Low-pass filter (H) coefficients
Haar	2	g[0] = −0.7071067812	h[0] = 0.7071067812
		g[1] = 0.7071067812	h[1] = 0.7071067812
Symlet2	4	g[0] = −0.4829629131	h[0] = −0.1294095226
		g[1] = 0.8365163037	h[1] = 0.2241438680
		g[2] = −0.2241438680	h[2] = 0.8365163037
		g[3] = −0.1294095226	h[3] = 0.4829629131
Biortho- gonal 1.3	6	g[0] = 0	h[0] = −0.0883883476
		g[1] = 0	h[1] = 0.0883883476
		g[2] = −0.7071067812	h[2] = 0.7071067812
		g[3] = 0.7071067812	h[3] = 0.7071067812
		g[4] = 0	h[4] = 0.0883883476
		g[5] = 0	h[5] = −0.0883883476
Daubechies4	8	g[0] = −0.2303778133	h[0] = −0.0105974018
		g[1] = 0.7148465706	h[1] = 0.0328830117
		g[2] = −0.6308807679	h[2] = 0.0308413818
		g[3] = −0.0279837694	h[3] = −0.1870348117
		g[4] = 0.1870348117	h[4] = −0.0279837694
		g[5] = 0.0308413818	h[5] = 0.6308807679
		g[6] = −0.0328830117	h[6] = 0.7148465706
		g[7] = −0.0105974018	h[7] = 0.2303778133

The inverse DWT (IDWT) reconstructs a^j from a^j + 1 and d^j + 1 by up-sampling by a factor of two and convolving the results by the reconstructed filter. The original signal (x[n]) can be recovered by iteratively continuing the IDWT algorithm. IDWT is not interesting for APs detection, that’s why we don’t use it. It is then possible to take approximations toward filters orthogonality and filter coefficients.