The 6th-order lowpass Chebyshev filter of Ex. 7.21 can be realized as a single-section direct form system with transfer function
As in Ex. 7.21, assume that
(a) Determine the 13 coefficients comprising H(z), and generate a pole-zero plot for this system.
(b) Plot the magnitude response |H(ejΩ)| over 0 ≤ Ω/T ≤ 100, and verify that it matches Fig. 7.36.
(c) Quantize the 13 coefficients comprising H(z) using 12-, 10-, 8-, and 6-bit word lengths. Present your results in a form similar to Table 7.3.
(d) Investigate 12-, 10-, 8-, and 6-bit coefficient quantization on the locations of the system poles and zeros. Identify those cases, if any, that produce realizations that are not stable. (e) Investigate 12-, 10-, 8-, and 6-bit coef- ficient quantization on the magnitude response of this system. Identify those cases, if any, that produce realizations that do not closely match the original filter. (f) Determine the smallest word length that produces a realization that essentially matches the original filter. Hint: The smallest word length may be a value other than 12, 10, 8, or 6.