The impulse response of a discrete-time system is h[n] = ( 0.5) n u[n]. (a) If
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The impulse response of a discrete-time system is h[n] = ( − 0.5)n u[n].
(a) If the input of the system is x[n] = δ[n] + δ[n − 1] + δ[n − 2], use the linearity and time-invariance of the system to find the corresponding output y[n].
(b) Find the convolution sum corresponding to the above input, and show that your solution coincides with the output y[n] obtained above.
(c) Use the function conv to find the output y[n] due to the given input x[n]. Plot x[n], h[n], and y[n] using.
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