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3. For each impulse response below, determine whether the corresponding system is (i) Memoryless (ii) Causal and (iii) Stable (a) h(t)=u(t+1) (b) h(t)=cos(?t) 4. Find the convolution y[n]=x[n]h[n] of the following signals by using graphical method. where x[n]={-1,-2,-1,4}, and h[n]={-4,2,3,-1} . Draw x[n], h[n] and the output signal y[n]. 5. Calculate the following convolution integral, y(t)=x(t)h(t)=e^{-3t}u(t) * u(t + 3). Sketch the relevant signal graph to arrive at your answer.

          3. For each impulse response below, determine whether the corresponding system
is (i) Memoryless (ii) Causal and (iii) Stable

(a) h(t)=u(t+1)
(b) h(t)=cos(?t)

4. Find the convolution y[n]=x[n]*h[n] of the following signals by using graphical
method. where x[n]={-1,-2,-1,4}, and h[n]={-4,2,3,-1} . Draw x[n], h[n] and the
output signal y[n].

5. Calculate the following convolution integral, y(t)=x(t)*h(t)=e^{-3t}u(t) * u(t + 3).
Sketch the relevant signal graph to arrive at your answer.

Show more…

3. For each impulse response below, determine whether the corresponding system
is (i) Memoryless (ii) Causal and (iii) Stable

(a) h(t)=u(t+1)
(b) h(t)=cos(?t)

4. Find the convolution y[n]=x[n]*h[n] of the following signals by using graphical
method. where x[n]=-1,-2,-1,4, and h[n]=-4,2,3,-1 . Draw x[n], h[n] and the
output signal y[n].

5. Calculate the following convolution integral, y(t)=x(t)*h(t)=e^-3tu(t) * u(t + 3).
Sketch the relevant signal graph to arrive at your answer.

Added by Heather A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

07/27/2024

Step 1

(a) \( h(t) = u(t+1) \) - Memoryless: No, because the output depends on past values of the input. - Causal: No, because \( u(t+1) \) is non-zero for \( t < 0 \). - Stable: Yes, because the unit step function is bounded. (b) \( h(t) = \cos(t) \) - Memoryless: Show more…

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For each impulse response below, determine whether the corresponding system is i) Memoryless, ii) Causal, and iii) Stable. (a) h(t) = u(t+1) (b) h(t) = cos(̀t) Find the convolution y[n] = x[n] * h[n] of the following signals by using the graphical method. Where x[n] = {-1, -2, -1, 4}, and h[n] = {-4, 2, 3, -1}. Draw x[n], h[n], and the output signal y[n]. Calculate the following convolution integral, y(t) = x(t) * h(t) = e^(-3t)u(t) * u(t + 3). Sketch the relevant signal graph to arrive at your answer.

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