DirectForm I
As mentioned in §5.5, the difference equation(10.1) 
specifies the DirectForm I (DFI) implementation of a digital filter [60]. The DFI signal flow graph for the secondorder case is shown in Fig.9.1.
The DFI structure has the following properties:
 It can be regarded as a twozero filter section followed in series by a twopole filter section.
 In most fixedpoint arithmetic schemes (such as two's complement, the most commonly used [84]^{10.1}) there is no possibility of internal filter overflow. That is, since there is fundamentally only one summation point in the filter, and since fixedpoint overflow naturally ``wraps around'' from the largest positive to the largest negative number and vice versa, then as long as the final result is ``in range'', overflow is avoided, even when there is overflow of intermediate results in the sum (see below for an example). This is an important, valuable, and unusual property of the DFI filter structure.
 There are twice as many delays as are necessary. As a result, the DFI structure is not canonical with respect to delay. In general, it is always possible to implement an thorder filter using only delay elements.
 As is the case with all directform filter structures (those which have coefficients given by the transferfunction coefficients), the filter poles and zeros can be very sensitive to roundoff errors in the filter coefficients. This is usually not a problem for a simple secondorder section, such as in Fig.9.1, but it can become a problem for higher order directform filters. This is the same numerical sensitivity that polynomial roots have with respect to polynomialcoefficient roundoff. As is well known, the sensitivity tends to be larger when the roots are clustered closely together, as opposed to being well spread out in the complex plane [18, p. 246]. To minimize this sensitivity, it is common to factor filter transfer functions into series and/or parallel secondorder sections, as discussed in §9.2 below.
Two's Complement WrapAround
In this section, we give an example showing how temporary overflow in two's complement fixedpoint causes no ill effects. In 3bit signed fixedpoint arithmetic, the available numbers are as shown in Table 9.1.

Let's perform the sum , which gives a temporary overflow (, which wraps around to ), but a final result () which is in the allowed range :^{10.3}
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Direct Form II
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OnePole Transfer Functions