Impulse Response Descriptions Exercises

The impulse response of a system is the output when the input is a(n) $\_\_\_\_\_\_\_\_\_\_\_$  signal.

The impulse response allows you to determine the output for any input if the system is linear and time invariant.

Express the signal depicted below as the weighted sum of time-shifted impulses.

Consider applying $x[n]$ to a LTI system with impulse response

$h[n] = \left\{\begin{array}{cl} 1 & n= 0,1,2,3\\ 0 & n \mbox{otherwise} \end{array} \right.$

as shown in the figure below.

Find the output $y_{-1}[n]$ due to the component of $x[n]$ associated with $\delta[n+1]$.

Consider applying $x[n]$ to a LTI system with impulse response

$h[n] = \left\{\begin{array}{cl} 1 & n= 0,1,2,3\\ 0 & n \mbox{otherwise} \end{array} \right.$

as shown in the figure below.

Find the output $y_{1}[n]$ due to the component of $x[n]$ associated with $\delta[n-1]$.

Consider applying $x[n]$ to a LTI system with impulse response

$h[n] = \left\{\begin{array}{cl} 1 & n= 0,1,2,3\\ 0 & n \mbox{otherwise} \end{array} \right.$

as shown in the figure below.

Find the output $y_{2}[n]$ due to the component of $x[n]$ associated with $\delta[n-2]$.

Consider applying $x[n]$ to a LTI system with impulse response

$h[n] = \left\{\begin{array}{cl} 1 & n= 0,1,2,3\\ 0 & n \mbox{otherwise} \end{array} \right.$

as shown in the figure below.

Find the output $y_{4}[n]$ due to the component of $x[n]$ associated with $\delta[n-4]$.

Consider applying $x[n]$ to a LTI system with impulse response

$h[n] = \left\{\begin{array}{cl} 1 & n= 0,1,2,3\\ 0 & n \mbox{otherwise} \end{array} \right.$

as shown in the figure below.

Find the output $y[n]$.

Problem statements in pdf file here.  Note there are some differences from the quiz questions to map them onto the quiz tool.