Introduction to Digital Filters by Trevor J. Terrell (auth.)
By Trevor J. Terrell (auth.)
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Example text
However, some types of recursive digital fllter have non-linear phase characteristiCs which may produce unacceptable waveform distortion. The linear phase characteristic of the frequency sampling fllters discussed in this chapter, and the fact that this type of fllter has integer coefficients makes this an attractive, economical and useful recursive digital fllter in some simple applications. 2 INDIRECT APPROACH USING PROTOTYPE CONTINUOUS FILTER In general the design of a prototype continuous (analogue) fllter involves two main steps, namely (I) firstly deriving a realisable transfer function, G(S); and (2) subsequently synthesising the transfer function.
3) n For a stable Butterworth ftlter the transfer function, G(S) is a rational function having a numerator equal to unity and denominator determined by selecting the 43 Design of Recursive Digital Filters roots of 1 + (-1tS 2 n that are located in the left-hand half of the S-plane. Note that mirror images of the poles of G(S) exist in the right-hand half of the S-plane, and we associate these with G( -S). To illustrate the method of determining G(S) an example will now be considered. 1 Suppose that to meet a given filter specification the order of the filter must be n = 3.
W. Tukey, 'An Algorithm for the Machine Calculation of Complex Fourier Series',Mathematics of Computing, 19 (1965} 297-301. 2. J. F. Kaiser, 'Design Methods for Digital Filters', Proceedings of the First Allerton Conference on Circuit and System Theory, (1963) 221-36. 3. R. Rabiner and C. M. Rader,Digital Signal Processing (IEEE Press, New York, 1972). 4. H. D. Helms and J. F. Kaiser, Literature in Digital Signal Processing (IEEE Press, New York, 1975}. 5. J. A. , 1973). 6. J. R. Ragazzini and G.