Consider the two discrete time signals y = f(t) and y = g(t) graphed below and each sampled 8 times per second for 0 \leq t \leq 1 .

Graph of |
Graph of |

- Find the coordinate vector representations for the discrete time signals
f(t) andg(t) .\vec{f}= help (vectors) \vec{g}= help (vectors)

- Draw the vector sum
\vec{f} + \vec{f} as a discrete time signal. Then, verify your answer using vector addition operations.\vec{f} + \vec{g} = help (vectors)

- Draw the scaled vector
-4 \vec{f} as a discrete time signal. Then, verify your answer using vector addition operations.-4 \vec{f} = help (vectors)

- Find the vector sum
k_1 \vec{f} + k_2 \vec{g} whenk_1 = -2 andk_2 = 3 .k_1 \vec{f} + k_2\vec{g} = help (vectors)

- Find the additive inverse of
\vec{g} .\vec{g} + = \mathbf{0}. help (vectors)

You can earn partial credit on this problem.