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, masking such issues as microprocessors-based filters, single-chip DSP units, machine processing of 2-dimensional indications and VLSI sign processing.

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42) g(i)T W' =0,1 ,2, ... , (N- 1), where Gr=G(eiwrT) and W=e-j2rr/N However, Wr = w 5 r/N and therefore the DFT is a periodic function in the frequency domain, with a period of 21T/T rad/s. Introduction 33 It is possible to reverse the transformation to obtain g( i)T values from a sampled frequency spectrum, G,. This process is achieved by applying the inverse discrete Fourier transform (IDFT), which is defined as 1 N-1 g(i)T = - - ~ N r=O i =0,1 ,2, ... 18 using the DFT method. Comment on the result.

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. 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. Cadzow, Discrete Time Systems: An Introduction with Interdisciplinary Applications (Prentice-Hall, Englewood Cliffs, NJ, 197 3).

Bergland, 'A Guided Tour of the Fast Fourier Transform', IEEE Spectrum, 6 (1969) 41-52. 10. J. T. Tou, Digital and Sampled-data Control Systems (McGraw-Hill, New York. 1959). 11. C. S. Burrus and T. W. Parks, DFT/FFT Convolution Algorithms: Theory and Implementation (Wiley, New York and London, 1985). 4}. 3 Determine the Z-transform and region of convergence for f(n) = {Ctt 0 for n;;;;. 25). Determine: (a) a general expression for the filter's unit-step response, and evaluate it at the first four sampling instants; and (b) a general expression for the filter's unit-impulse response, and use it in the convolution-summation representation to verify the unit-step values calculated in part (a).

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