Please solve these questions. Thank you. 16.3 (a) Use the impulse invariance method to show that the analog transfer function given by XXXXXXXXXXH(s)=3+2.7747s2 +3.8494s XXXXXXXXXXB. Friedlander and...

Please solve these questions. Thank you.

16.3 (a) Use the impulse invariance method to show that the analog transfer function given by 2.6702 H(s)=3+2.7747s2 +3.8494s +2.6702 B. Friedlander and B. Porat, the modified Yule-Walker method of ARMA spectral estimation, IEEE Transactions on Aerospace Electronic Systems (1984), AES-20(2), 158-173. (2] L. B. Jackson, Digital Filters and Signal Processing. 3rd edn. Kluwer Academic Publishers (1996), Chap. 10, pp. 345-355 16 lIR filter design results in the following z-transfer function: 0.4695220.1907z H(z)=3-0.610622 +0.3398z- 0.0624 as stated in Example 16.3 for the third-order Butterworth filter. (b) Use the impulse invariance method to show that the analog transfer function given by 6.2902 H(s) +4.1 383s3+8.5630s2 + 10.3791s +6.2902 results in the following z-transfer function: 0.3298z30.4274z20.0427z H(z) z4-0.4978z3 0.3958z2 - 0.1197z 0.0159 = as stated in Example 16.3 for the fourth-order Butterworth filter.