The discrete wavelet transform, the undecimated wavelet transform, and wavelet packet analysis use filter banks, as shown in the following illustration:

G1(z) is the analysis highpass filter. G0(z) is the analysis lowpass filter. G1(z) and G0(z) form the analysis filter bank. The output of the analysis highpass filter are the detail coefficients. The output of the analysis lowpass filter are the approximation coefficients. H1(z) is the synthesis highpass filter. H0(z) is the synthesis lowpass filter. H1(z) and H0(z) form the synthesis filter bank.