Translations:Wavelets - book/7/en

Recall our discussion in Chapter 4, in which we mentioned the three types of wavelets: causal, noncausal, and purely noncausal wavelets. Now we will learn more about them. Also recall that in Chapter 5, we saw that a digital filter is represented by a sequence of numbers called its impulse response or its weighting coefficients. A digital filter is said to be causal if its present output (at time n) depends only on present and past inputs (that is, depends only on inputs at times n, n – 1, n – 2, … , and so on. Another term for a causal filter is a realizable filter. In equation 2 of Chapter 5, we saw that the most general causal filter with a finite number of delay elements has the form