Let h[n] be the impulse response of the system y[n] = a[n]y[n-1]. (a) Find the impulse...

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Let h[n] be the impulse response of the system y[n] = a[n]y[n-1]. (a) Find the impulse response h[n] of this system. Is it BIBO stable? Is it causal? (b) Let the series cascade of M systems with impulse response h[n] as in Problem 4a be hu[n]. What is the minimum value of M for which hm[n] → ∞o, as n → ∞o? (c) The system is modified to y[n] = a[n] ay[n-1], (8) to improve stability. Let g[n] be the impulse response for this filter. As a designer, what values of a will you choose to make the system BIBO stable? Let h[n] be the impulse response of the system y[n] = a[n]y[n-1]. (a) Find the impulse response h[n] of this system. Is it BIBO stable? Is it causal? (b) Let the series cascade of M systems with impulse response h[n] as in Problem 4a be hu[n]. What is the minimum value of M for which hm[n] → ∞o, as n → ∞o? (c) The system is modified to y[n] = a[n] ay[n-1], (8) to improve stability. Let g[n] be the impulse response for this filter. As a designer, what values of a will you choose to make the system BIBO stable?

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