Introduction to Digital Filters by Trevor J. Terrell (auth.)
By Trevor J. Terrell (auth.)
In this revised and up-to-date variation specific consciousness has been paid to the sensible implementations of electronic filters, protecting such subject matters as microprocessors-based filters, single-chip DSP units, desktop processing of 2-dimensional signs and VLSI sign processing.
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Sample text
19 Two-dimensional DFT resulting from a series of 1-D column and row DFTs ~n, +4 ,,~ +4 r, Ul CD .... ;:; ::!! c =·=!!. Cl ::I c;· = n - Cl Cl. = -.... o :::1 c;· ~ c:: Q, a a 50 Introduction to Digital Filters REFERENCES 1. J. W. Cooley and J. W. Tukey, 'An Algorithm for the Machine Calculation of Complex Fourier Series',MathematicsofComputing, 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.
That is, in using this approach we will firstly obtain a suitable transfer function, G(S), and then derive the corresponding pulse transfer function, G(Z), using one of the Z-transform methods discussed later in this chapter. I. 1 Indirect approach to the design of digital fJlters In order to carry out step (1), that is, in going from the fJlter specification to the transfer function G(S), it will be necessary to consider the design of continuous filters, and in particular Butterworth and Chebyshev fJlters will be briefly reviewed since both types are commonly used in this approach to digital fJlter design.
__ .. g(3)' g(3)' ¥"" g(O) g(3)' g(5) g(5) g(4) g(4) G2(0) g(O) g(3)' X "' G 3 (7) g(4) ~ " / "' bit-reversed shuffling J '- g(3)' l. 13 Interconnected butterflies for an eight-point decimation-in-frequency FFT g(7) g(6)/ X.. g(3)' g(4) g(O) g(3)' g(4) g(4) g(4) g(5) G 1 (0) g(O) g(3)' g(O) g(3)' J G(7) ~G(6) e G(5) ". g(4)G(4) g(4) g(3)' J1 G(3) g(3)' G(2) g(5) g(5) G(l) g(4) g(4) G(O) g(O) g(3)' g(O) g(3)' ~ -=· ... :::!! en CD ::; t» :::;: Cl Cl ::I c;· n c:: Cl a. -=... - Cl g(7) g(6) } , '< '' r, ....