The design and application of four-tap wavelet filters

The design of a simple four-tap filter is considered. The simplest four-tap low-pass filter, the four term averager, has the coefficients 1/2, 1/2, 1/2, 1/2. Chosen for their simplicity and also because the low-pass filter is then orthogonal to its complementary highpass filter. This general design allows the properties of the magnitude and phase responses to be readily determined