A digital system is described by the following difference equation: y[n] = x[n] - 0.3 x[n-1] + 0.28 x[n-2] Find the transfer function H(z), the denominator polynomial A(z), and the numerator polynomial B(z). Repeat Example #6 (from Week #4 Notes) but solve for the impulse response instead of the step response. An IIR system is expressed as y[n] = 0.5 x[n] + 0.2 y[n-1]
a. Find H(z).
b. Find the system response y[n] due to the input x[n] = (0.5)n u[n]. Given the first-order IIR system H(z) = (1 + 2z-1) / (1 - 0.5z-1) Realize and develop the difference equations using the following forms: a. Direct-form I b. Direct-form II