# Category: signal processing and linear systems #### 8. [4 points] The following are the impulse response of discrete-time LTI system. Determine whether each system is casual and/or stable. Justify your answers.

... #### 7. [3 points] The following are the impulse response of continuous-time LTI systems. Determine whether each system is casual and/or stable. Justify your answers.

... #### 6. [3 points] The input-output pair shown in the figure below is given for an LTI system

... #### 5. [2 points] Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to the input x(t).Sketch your results.

... #### 4. [3 points] An LTI system has impulse response defined by

... #### 3. [3 points]Let x(t) =u(t – 3) -u(t – 5) and h(t) = e^-3t u(t)

... #### 2. Compute and plot each of the following three convolutions:

... #### 1. [4 points] MARLAB Exercise: Use the-in conv() function of MATLAB to compute the convolution between the input x[n] and impulse response h[n] shown below. Submit MATLAB script that makes stem() plots of the input, impulse response, and the output. Plot the output in your answer sheet.

... #### Determine the discrete-time Fourier transform (DTFT) X(Ωk ) of the discrete-time signal ̃x[n] = sin(0.4πn). Also, show your calculation for X(Ω1 ) and X(Ω4 ) . Given, x[n] = u[n] u[n + 1] and h[n] = (0.5) n DTFTs: a) X(Ω), b) H(Ω), and c) Y (Ω)

... #### For the system of Figure P6.27, sketch and Show all ampli- tudes and frequencies.

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