Question 3: For a given discrete system input and output relation is given as $y[n] = (2n - 1)e^{x[\frac{n}{2}]}$ a) Is this system memoryless? (4p) b) Is this system causal? (4p) c) Is this system BIBO stable? (4p) d) Is this system linear? (4p) e) Is this system time invariant? (4p)
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Problem 2 Determine whether each of the discrete-time systems below is: (a) linear, (b) shift-invariant, (c) causal, and (d) BIBO stable: (i) y[n] = (n+1)/x[n] (ii) y[n] = sin(x[n + 1]) (iii) y[n] = max{x[n - 1], x[n], x[n + 1]} (iv) y[n] = ̓∑_{k=-∞}^{n} x[k].
Adi S.
Q2: (30 pts) Given the following system: y[n] = a^n x[n] u[n], 1 > a > 0 Determine whether the system is: a) Stable b) Causal c) Linear d) Time-Invariant Justify your answers. Q3: (30 pts) Given the following system: y[n] = e^{x[n]} Determine whether the system is: a) Stable b) Causal c) Invertible d) Linear e) Time-Invariant Justify your answers.
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