Question

2.45,2.48 explain clearly please

Signals and Systems: A Primer with MATLAB 104 20 1H y(t) x(t) FIGURE 2.38 For Problem 2.48. 2.45 An accumulator has impulse response h[n] = u[n]. Check if an accumulator is BIBO stable 2.46 The input to the circuit discussed in Example 2.15 is v,) ut - )dt - 2) Use convolution to determine the output 2.47 Determine the output of the circuit discussed in Practice Problem 2.15 if v,) u() 2.48 If the filter in Figure 2.38 has the impulse response h) 5)-2eu), find the step response.

Answer 1

Ans 2.45) h[n] = u [n]. for the BTBo stability, the necessary and malbad <co sufferent condition is that In cw Cose- - ادا ادمای ...... to times . = thit o. Ž Ihan] and So, the necessary and sufficient condition of BIBU stability is not satished hence the system with h = un] is BIBb unstable. This can be intuitively understood by applyng an input of alna uG] which is bounded. The autput is then yG = an hond = un] *u [n] = r[n] which is a unit ramp function and is unbounded) J.

Ans 2.8) (t) = S(t) - ze stact). The input is a unit step input for fronding the step response. act) = uct) The will use la place transform to calculate y (t) = hct) Ct) as we would be able to aud integration HCS) - h{bct)} 2 { SCH) - 2e-stuct)} = 2 Esct)}- 2x 2 {e- 2t (t)} = 1-2x L (5+2 / [By linearity property of Laplace transform]

..HG) = 1-2 S+2 .HC) =s - st2 W X© 2{act)? =hluct)} ExG) - L - YG) - HC)x() - -[from W) and Cu).] .: Y(s) = 1 S+2 1. y(t) = 2 - {Y()} =hts in J [st2 lyct) - 9ct)