- A Real Time System Comprises A Cascade Of Two Discrete Time Filters The First Filter With Impulse Response H N Is De 1 (35.05 KiB) Viewed 31 times
A real-time system comprises a cascade of two discrete-time filters. The first filter, with impulse response h[n], is defined by the pole-zero plot for H(z) shown below, along with the information that h[0] = 2. y[n] x{n}- h[n] g[n] z[n] a) Find h[n]. b) Find the difference equation of a second system, characterized by g[n], such that z[n] = x[n].
0.5 0 -0.5 -1 X H(₂) O O -1 -0.5 0 0.5 1 Solution: H(-) = √(-+)(-++/) - 12+ - +++ - (¹2) (= = A = A· = 1–4:² The value of A is found by noting that this is a causal system, so h[0] = lim H(z) = A=2, and 2 2 4 H(=) = −2+; 1- + =&=* *1+}=* Hence, h[n]=_28[n]+2(f" +(-±) \u n b) The inverse system is G(=) = so the corresponding difference equation is __y{[n]++y[n−2] = $x[n]−}x[n=2]