Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let d = 3, a = 0.4, b = 0.5, c = 0.8. Design an inverse filter h2[n] so that the y[n] = x[n] Find H2(z) Derive ћ2ml by taking inverse Ž tranform of H2Izj In this case, is h2[n] an FIR or an IIR filter? Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let d = 3, a = 0.4, b = 0.5, c = 0.8. Design an inverse filter h2[n] so that the y[n] = x[n] Find H2(z) Derive ћ2ml by taking inverse Ž tranform of H2Izj In this case, is h2[n] an FIR or an IIR filter?


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