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2. a) Consider a stable, first order, causal IIR filter of the following general form: y(n) + ay(n-1)= box(n) +bx(n-1). Assuming it has the following properties, find its transfer function, H(z): i. It annihilates signals of the form, (0.9)Pu(n). ii. Its unit impulse response is of the form, h(n)= co(0.5)u(n) + ci(0.5)"lu(n-1), where co and ci are some constants. iii. Also, H(@)-= = 1. b) What is the steady state output of the above system due to the following input: x(n)=2cos(0.75an)u(n) - 3u(n) 2. a) Consider a stable, first order, causal IIR filter of the following general form: y(n) + ay(n-1)= box(n) +bx(n-1). Assuming it has the following properties, find its transfer function, H(z): i. It annihilates signals of the form, (0.9)Pu(n). ii. Its unit impulse response is of the form, h(n)= co(0.5)u(n) + ci(0.5)"lu(n-1), where co and ci are some constants. iii. Also, H(@)-= = 1. b) What is the steady state output of the above system due to the following input: x(n)=2cos(0.75an)u(n) - 3u(n)