Introduction to Digital Filters by Trevor J. Terrell (auth.)

By Trevor J. Terrell (auth.)

In this revised and up-to-date version specific realization has been paid to the sensible implementations of electronic filters, overlaying such issues as microprocessors-based filters, single-chip DSP units, computing device processing of 2-dimensional indications and VLSI sign processing.

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G. D. 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).

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). 2 Determine: (a) the location, in the Z-plane, of the filter's poles and zeros; (b) whether or not the filter is stable; (c) a general expression for the filter's unitimpulse response; (d) the filter's linear difference equation; (e) the frequency response of the filter at a frequency equal to one half of the sampling frequency; and (f) the frequency response of the filter obtained via the DFT for N = 4.

35 we obtain X(Z) [a 0 +a 1 z-l +a 2 z- 2 + ... +an z-n] Y(Z) [ 1 +bt z-t +b 2 z- 2 + .. 35, Y(Z) is then seen to be equal to G(Z). Hence we see that the Z-transform of the filter's unit-impulse response is equal to the pulse transfer function. Conversely the inverse Z-transform of the pulse traasfer function yields the impulse response (weighting sequence), g(i)T, of the filter. 5). Determine (a) a general expression for the filter's unit-step response, and calculate the output values at the first, second and third sampling instants, and (b) a general expression for the filter's unit-impulse response, using it in the convolution-summation representation method to verify the unit-step response values calculated in part (a).

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