Synthesis of IIR digital filters exhibiting simultaneous amplitude and phase responses for VLSI implementations
✍ Scribed by Abo-Zahhad, M.; El-Raheem, G. A.; Fahmy, M. F.
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 740 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0098-9886
No coin nor oath required. For personal study only.
✦ Synopsis
In the literature there are many papers that deal with the combined approximation of loss and phase (and or group delay) characteristics. 1 -12 Unfortunately, many of these approaches are non-optimum in the sense that the filter specifications can be satisfied with a lower-degree filter. Optimal solutions to the approximation problem are those that use all the available degrees of freedom in controlling the filter characteristics. 1,2 This means that for an nth-degree filter, 2n + 1 conditions should be satisfied by the filter transfer function. As an example, the solution reported in Reference 3 for the design of digital, sampled-data and non-reciprocal lumped filters is a non-optimum solution. In that paper, n -r + 1, n -r and r conditions are devoted to the passband amplitude, passband phase and stopband amplitude respectively. Consequently, r degrees of freedom are not used. In some other available optimal solutions, either selectivity is poor 4,5 or stability of the resulting transfer functions is not always guaranteed. 3 This motivates the search for alternative solutions for such filters and consequently leads to the introduction of arbitrary linear phase polynomials. 6 -10 More recently, two methods have been described for the design of selective filters with a finite band approximation to constant amplitude and delay together with an arbitrary number of transmission zeros at infinity. 11,12 In this paper the solution obtained in Reference 12 is extended to include filters with an arbitrary number of transmission zeros at finite frequencies. All the available degrees of freedom are used and are distributed between the passband amplitude, passband phase and stopband attenuation in an arbitrary manner. This means that optimal solutions with a great deal of flexibility in shaping the amplitude and delay responses can be obtained.
It remains to digitally implement the resulting transfer function in a form that is suitable for VLSI implementations. That is, in addition to classical criteria of low sensitivity with respect to finite word length and absence of limit cycle and overflow oscillations, the filter structure should have the following properties. 13 -15 1. The structure should be of the concurrent array processor type, i.e. a cascaded interconnection of identical processors with only nearest-neighbour links.